@unpublished {bhar2026IMAGEolr,
	title = {OpenSeisML: Open Large-Scale Real Seismic and well-log Dataset for Generative AI},
	year = {2026},
	month = {3},
	abstract = {The advent of machine learning (ML) and computer vision has significantly accelerated seismic inversion workflows by reducing the computational cost of traditionally expensive iterative methods. However, the development and evaluation of ML methods remains limited by the scarcity of realistic velocity models, as most high-quality data are privately owned by oil and gas companies. To address this gap, we present *OpenSeisML*, a collection of real seismic datasets designed to support generative AI (Gen-AI) workflows for seismic inversion. The datasets are curated from publicly available surveys in the UK National Data Repository (NDR). When seismic volumes are in the time domain and wells are in depth, a time-to-depth conversion is required. We use checkshot data to establish the time{\textendash}depth relationship and construct a velocity model through interpolation for accurate conversion of post-stack seismic data. Here, we present an automated data curation pipeline that enables seismic data preparation while ensuring reproducibility. The objective is to train a generative model that captures the statistical distribution of subsurface properties, enabling the synthesis of multiple statistically consistent realizations for uncertainty quantification which can act as a prior for seismic inversion.},
	keywords = {deep learning, generative model, IMAGE, Imaging, Inverse problems, real seismic data, SEG, time-to-depth conversion, well logs, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/bhar2026IMAGEolr/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/2026IMAGEolr/IMAGE_Ipsita.pdf},
	author = {Ipsita Bhar and Huseyin Tuna Erdinc and Thales Souza and Charles Jones and Felix J. Herrmann}
}
@unpublished {erdinc2026IMAGEsai,
	title = {SAGE: Subsurface AI-driven Geostatistical Extraction with proxy posterior},
	year = {2026},
	month = {3},
	abstract = {Recent advances in generative networks have enabled new approaches to subsurface velocity model synthesis, offering a compelling alternative to traditional methods such as Full Waveform Inversion. However, these approaches predominantly rely on the availability of large-scale datasets of high-quality, geologically realistic subsurface velocity models, which are often difficult to obtain in practice. We introduce SAGE, a novel framework for statistically consistent proxy velocity generation from incomplete observations, specifically sparse well logs and migrated seismic images. During training, SAGE learns a proxy posterior over velocity models conditioned on both modalities (wells and seismic); at inference, it produces full-resolution velocity fields conditioned solely on migrated images, with well information implicitly encoded in the learned distribution. This enables the generation of geologically plausible and statistically accurate velocity realizations. We validate SAGE on both synthetic and field datasets, demonstrating its ability to capture complex subsurface variability under limited observational constraints. Furthermore, samples drawn from the learned proxy distribution can be leveraged to train downstream networks, supporting inversion workflows. Overall, SAGE provides a scalable and data-efficient pathway toward learning geological proxy posterior for seismic imaging and inversion. Repo link: https://github.com/slimgroup/SAGE."},
	keywords = {Bayesian inference, deep learning, generative model, IMAGE, Imaging, Inverse problems, RTM, SAGE, score, SEG, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Submitted/2026/erdinc2026IMAGEsai/abstract.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Submitted/2026/erdinc2026IMAGEsai/IMAGE_Tuna.pdf},
	author = {Huseyin Tuna Erdinc and Ipsita Bhar and Rafael Orozco and Thales Souza and Felix J. Herrmann}
}
@article {orozco2024IPaspire,
	title = {ASPIRE: Iterative Amortized Posterior Inference for Bayesian Inverse Problems},
	journal = {Inverse Problems},
	volume = {41},
	year = {2025},
	note = {(Inverse Problems)},
	month = {3},
	abstract = {Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances in machine learning and variational inference (VI) have lowered the computational barrier by learning from examples. Two VI paradigms have emerged that represent different tradeoffs: amortized and non-amortized. Amortized VI can produce fast results but due to generalizing to many observed datasets it produces suboptimal inference results. Non-amortized VI is slower at inference but finds better posterior approximations since it is specialized towards a single observed dataset. Current amortized VI techniques run into a sub-optimality wall that can not be improved without more expressive neural networks or extra training data. We present a solution that enables iterative improvement of amortized posteriors that uses the same networks architectures and training data. The benefits of our method requires extra computations but these remain frugal since they are based on physics-hybrid methods and summary statistics. Importantly, these computations remain mostly offline thus our method maintains cheap and reusable online evaluation while bridging the approximation gap these two paradigms. We denote our proposed method ASPIRE - Amortized posteriors with Summaries that are Physics-based and Iteratively REfined. We first validate our method on a stylized problem with a known posterior then demonstrate its practical use on a high-dimensional and nonlinear transcranial medical imaging problem with ultrasound. Compared with the baseline and previous methods from the literature our method stands out as an computationally efficient and high-fidelity method for posterior inference.},
	keywords = {Amortization Gap, Amortized Variational Inference, Bayesian inference, medical imaging, Normalizing flows, simulation-based inference},
	doi = {10.1088/1361-6420/adba3d},
	url = {https://doi.org/10.1088/1361-6420/adba3d},
	author = {Rafael Orozco and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@conference {herrmann2025EAGEssf,
	title = {SAGE {\textemdash} Subsurface foundational model with AI-driven Geostatistical Extraction},
	booktitle = {EAGE Workshop},
	year = {2025},
	month = {6},
	abstract = {In this talk, we introduce a novel diffusion-based generative modeling approach for synthesizing high-fidelity subsurface velocity models. Once trained, this foundational model serves as a prior or a generative tool, enabling the sampling of velocity models that closely match the statistical distribution of geologically relevant Earth models. To achieve this, we leverage geostatistical information derived from curated datasets provided by the UK National Data Repository. Our training set comprises check-shot-corrected migrated images intersected by well logs. Numerical experiments on multiple synthetic datasets, including the Compass model and Synthoseis, demonstrate the model{\textquoteright}s ability to generate realistic subsurface velocity models. This capability offers a data-driven prior for full-waveform inversion and facilitates the generation of training samples for amortized neural networks to improve full-waveform inference.},
	keywords = {Bayesian inference, deep learning, EAGE, foundation models, full waveform inference, generative model, Imaging, Inverse problems, RTM, score, Summary Statistics, UK-NDR, Uncertainty quantification},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2025/herrmann2025EAGEssf/EAGE_WS22_Foundation_Herrmann.mp4},
	author = {Huseyin Tuna Erdinc and Thales Souza and Felix J. Herrmann}
}
@conference {erdinc2025ML4SEISMICspm,
	title = {SAGE - Subsurface modeling with AI-driven Geostatistical Extraction and evaluation on North Sea Data},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Traditional machine learning based approaches often depend on large, high-quality and complete datasets of 2D Earth propety models, which can be difficult to obtain in subsurface applications. In this study, we leverage score-based generative models to synthesize high-fidelity geophysical properties (velocity, density, etc.) trained on a combination of sparse but tied well logs and seismic lines without relying on densely sampled velocity models and adress the sampling-density differences by enabling coherent integration of these complementary sources of information. With experiments on multiple synthetic datasets from subsurface models featuring diverse geological structures (e.g., faults, salt bodies), we demonstrate that our approach can accurately capture long-range geological correlations and align well with unseen ground-truth properties. Finally, we highlight the potential of our method to generalize to field data by conducting fine-tuning on a curated dataset derived from real well-log and seismic data currated from the UK Data Repository for the North Sea. This study represents an important step toward the development of foundational models for inverting physical properties and provides inputs for applications such as full-waveform inference (WISE/ASPIRE), supervised learning algorithms, and enhanced seismic-based subsurface modeling.},
	keywords = {Bayesian inference, deep learning, generative model, Imaging, Inverse problems, ML4SEISMIC, North-sea data, power-scaling, RTM, score, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/erdinc2025ML4SEISMICspm},
	author = {Huseyin Tuna Erdinc and Ipsita Bhar and Thales Souza and Rafael Orozco and Felix J. Herrmann}
}
@conference {bhar2025ML4SEISMICsdc,
	title = {Seismic Dataset Curation from UK National Data Repository to Validate SAGE and WISE},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {This work presents a curated seismic dataset pipeline developed for data residing in the UK National Data Repository (UK NDR) in support of advanced generative geophysical modeling and machine learning. The workflow integrates checkshots and 3D post-stack seismic data volumes to generate accurate depth-domain seismic sections. Custom interpolation algorithms are used to construct velocity models from checkshot data, which are then used for time-to-depth conversion with [OpendTect]https://dgbes.com/software/opendtect. The converted seismic cubes are subsequently processed in Python using [SegySAK]https://segysak.readthedocs.io/en/latest/, a python package, enabling efficient extraction and visualization of 2D lines. These datasets will be used to further validate the workflow of SAGE (Subsurface foundational model for AI-driven Geostatistical Extraction), which focuses on large-scale representation learning for the geosciences. The trained generative models will be used as input to WISE and ASPIRE that form foundation models for seismic inference designed to characterize the subsurface. This curated dataset pipeline streamlines seismic data preparation, enhances reproducibility, and bridges the gap between conventional geophysical workflows and emerging data-driven inference methods.},
	keywords = {Bayesian inference, generative model, Imaging, ML4SEISMIC, North-sea data, RTM, SLIM, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/bhar2025ML4SEISMICsdc},
	author = {Ipsita Bhar and Huseyin Tuna Erdinc and Thales Souza and Rafael Orozco and Felix J. Herrmann}
}
@conference {herrmann2025SciMLtfm,
	title = {Towards foundation models for subsurface priors and posteriors},
	booktitle = {Workshop on Scientific Machine Learning 2025, Austin, TX},
	year = {2025},
	month = {9},
	keywords = {Bayesian inference, deep learning, foundation models, full waveform inference, generative model, Imaging, Inverse problems, RTM, SciML, score, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SciML/2025/herrmann2025SciMLtfm},
	author = {Huseyin Tuna Erdinc and Thales Souza and Shiqin Zeng and Rafael Orozco and Felix J. Herrmann}
}
@article {orozco2023invnet,
	title = {InvertibleNetworks.jl: A Julia package for scalable normalizing flows},
	journal = {Journal of Open Source Software},
	volume = {9},
	year = {2024},
	month = {7},
	abstract = {InvertibleNetworks.jl is a Julia package designed for the scalable implementation of normalizing flows, a method for density estimation and sampling in high-dimensional distributions. This package excels in memory efficiency by leveraging the inherent invertibility of normalizing flows, which significantly reduces memory requirements during backpropagation compared to existing normalizing flow packages that rely on automatic differentiation frameworks. InvertibleNetworks.jl has been adapted for diverse applications, including seismic imaging, medical imaging, and CO2 monitoring, demonstrating its effectiveness in learning high-dimensional distributions.},
	keywords = {Bayesian inference, computing, conditional normalizing flows, deep learning, HPC, Inverse problems, memory, Normalizing flows, software, Uncertainty quantification},
	doi = {10.21105/joss.06554},
	url = {https://doi.org/10.21105/joss.06554},
	author = {Rafael Orozco and Philipp A. Witte and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Bas Peters and Felix J. Herrmann}
}
@presentation {orozco2024ML4SEISMICmev,
	title = {Machine-learning enabled velocity-model building with uncertainty quantification},
	year = {2024},
	month = {11},
	abstract = {Accurately characterizing subsurface properties is crucial for a wide range of geophysical applications, from hydrocarbon exploration to monitoring of CO2 sequestration projects. Traditional characterization methods such as Full-Waveform Inversion (FWI) represent powerful tools but often struggle with the inherent complexities of the inverse problem, including noise, limited bandwidth and aperture of data, limited azimuth and computational constraints. To address these challenges, we propose a scalable methodology that integrates generative modeling with physics-informed summary statistics, making it suitable for complicated imaging problems potentially including field datasets. Our approach leverages the power of conditional diffusion networks, and methodologically incorporates physics in the form of summary statistics, allowing for the computationally efficient generation of Bayesian posterior samples that offer an useful assessment of uncertainty of the inferred migration-velocity models. To validate our approach, we introduce a battery of tests that measure the quality of the image estimates as well as the quality of the inferred uncertainties. With modern synthetic datasets, we maximally leverage the advantages of using subsurface-offset Common Image Gathers (CIGs) as the conditioning observable. Next, we tackle the challenging SEAM salt model that requires incorporating salt flooding into our approach based on the iterative refinements of ASPIRE {\textemdash} Amortized posteriors with Summaries that are Physics-based and Iteratively REfined.},
	keywords = {Amortized Variational Inference, Bayesian inference, deep learning, diffusion models, FWI, Imaging, Inverse problems, ML4SEISMIC, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/orozco2024ML4SEISMICmev},
	author = {Rafael Orozco and Huseyin Tuna Erdinc and Thales Souza and Yunlin Zeng and Ziyi Yin and Felix J. Herrmann}
}
@presentation {orozco2024ICLnwi,
	title = {Neural wave-based imaging with amortized uncertainty quantification},
	year = {2024},
	month = {6},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Imaging, Inverse problems, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICL/2024/orozco2024ICLnwi},
	author = {Rafael Orozco and Ziyi Yin and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@conference {orozco2024IPMSnwi,
	title = {Neural wave-based imaging with amortized uncertainty quantification},
	booktitle = {Inverse Problems: Modelling and Simulation},
	year = {2024},
	month = {5},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, deep learning, FWI, Imaging, Inverse problems, IPMS, MVA, RTM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/IPMS/2024/orozco2024IPMSnwi},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/IPMS/2024/orozco2024IPMSnwi/herrmann2024.pdf},
	author = {Rafael Orozco and Ziyi Yin and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@conference {zhang2023IMAGEssd,
	title = {3D seismic survey design by maximizing the spectral gap},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2023},
	note = {(IMAGE, Houston)},
	month = {08},
	abstract = {The massive cost of 3D acquisition calls for methods to reduce the number of receivers by designing optimal receiver sampling masks. Recent studies on 2D seismic showed that maximizing the spectral gap of the subsampling mask leads to better wavefield reconstruction results. We enrich the current study by proposing a simulation-free method to generate optimal 3D acquisition by maximizing the spectral gap of the subsampling mask via a simulated annealing algorithm. Numerical experiments confirm improvement of the proposed method over receiver sampling locations obtained by jittered sampling.},
	keywords = {Acquisition, matrix factorization, SEG, spectral gap, survey design, wavefield reconstruction},
	doi = {10.1190/image2023-3895546.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2023/zhang2023IMAGEssd/zhang2023IMAGEssd.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2023/zhang2023IMAGEssd/zhang2023IMAGEssd_pres.pdf},
	author = {Yijun Zhang and Ziyi Yin and Oscar Lopez and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@conference {orozco2022SPIEadjoint,
	title = {Adjoint operators enable fast and amortized machine learning based Bayesian uncertainty quantification},
	booktitle = {SPIE Medical Imaging Conference},
	year = {2023},
	note = {(SPIE, San Diego)},
	month = {02},
	abstract = {Machine learning algorithms such as Normalizing Flows, VAEs, and GANs are powerful tools in Bayesian uncertainty quantification (UQ) of inverse problems. Unfortunately, when using these algorithms medical imaging practitioners are faced with the challenging task of manually defining neural networks that can handle complicated inputs such as acoustic data. This task needs to be replicated for different receiver types or configurations since these change the dimensionality of the input. We propose to first transform the data using the adjoint operator {\textemdash}ex: time reversal in photoacoustic imaging (PAI) or back-projection in computer tomography (CT) imaging {\textemdash} then continue posterior inference using the adjoint data as an input now that it has been standardized to the size of the unknown model. This adjoint preprocessing technique has been used in previous works but with minimal discussion on if it is biased. In this work, we prove that conditioning on adjoint data is unbiased for a certain class of inverse problems. We then demonstrate with two medical imaging examples (PAI and CT) that adjoints enable two things: Firstly, adjoints partially undo the physics of the forward operator resulting in faster convergence of an ML based Bayesian UQ technique. Secondly, the algorithm is now robust to changes in the observed data caused by differing transducer subsampling in PAI and number of angles in CT. Our adjoint-based Bayesian inference method results in point estimates that are faster to compute than traditional baselines and show higher SSIM metrics, while also providing validated UQ.},
	keywords = {Amortized Inference, Bayesian inference, deep learning, Inverse problems, machine learning, medical imaging, Normalizing flows, SPIE, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SPIE/2023/orozco2022SPIEadjoint/SPIE_2022_adjoint.html},
	author = {Rafael Orozco and Ali Siahkoohi and Gabrio Rizzuti and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {orozco2023MIDLanf,
	title = {Amortized normalizing flows for transcranial ultrasound with uncertainty quantification},
	booktitle = {Medical Imaging with Deep Learning},
	year = {2023},
	note = {(MIDL, Nashville)},
	month = {07},
	abstract = {We present a novel approach to transcranial ultrasound computed tomography that utilizes normalizing flows to improve the speed of imaging and provide Bayesian uncertainty quantification. Our method combines physics-informed methods and data-driven methods to accelerate the reconstruction of the final image. We make use of a physics-informed summary statistic to incorporate the known ultrasound physics with the goal of compressing large incoming observations. This compression enables efficient training of the normalizing flow and standardizes the size of the data regardless of imaging configurations. The combinations of these methods results in fast uncertainty-aware image reconstruction that generalizes to a variety of transducer configurations. We evaluate our approach with in silico experiments and demonstrate that it can significantly improve the imaging speed while quantifying uncertainty. We validate the quality of our image reconstructions by comparing against the traditional physics-only method and also verify that our provided uncertainty is calibrated with the error.},
	keywords = {Bayesian Estimation, invertible networks, medical imaging, MIDL, Physics and Machine Learning Hybrid, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/MIDL/2023/orozco2023MIDLanf/paper.pdf},
	author = {Rafael Orozco and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Tristan van Leeuwen and Felix J. Herrmann}
}
@article {louboutin2023lmi,
	title = {Learned multiphysics inversion with differentiable programming and machine learning},
	journal = {The Leading Edge},
	volume = {42},
	year = {2023},
	note = {(The Leading Edge)},
	month = {07},
	pages = {452-516},
	abstract = {We present the Seismic Laboratory for Imaging and Modeling/Monitoring (SLIM) open-source software framework for computational geophysics and, more generally, inverse problems involving the wave-equation (e.g., seismic and medical ultrasound), regularization with learned priors, and learned neural surrogates for multiphase flow simulations. By integrating multiple layers of abstraction, our software is designed to be both readable and scalable. This allows researchers to easily formulate their problems in an abstract fashion while exploiting the latest developments in high-performance computing. We illustrate and demonstrate our design principles and their benefits by means of building a scalable prototype for permeability inversion from time-lapse crosswell seismic data, which aside from coupling of wave physics and multiphase flow, involves machine learning.},
	keywords = {CCS, deep learning, Fourier neural operators, GCS, Imaging, inversion, invertible networks, machine learning, monitoring, multiphysics, Normalizing flows, SLIM, software, time-lapse},
	url = {https://library.seg.org/doi/10.1190/tle42070474.1},
	presentation = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2023/louboutin2023lmi/le_software.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2023/louboutin2023lmi/le_software.html},
	author = {Mathias Louboutin and Ziyi Yin and Rafael Orozco and Thomas J. Grady II and Ali Siahkoohi and Gabrio Rizzuti and Philipp A. Witte and Olav M{\o}yner and Gerard J. Gorman and Felix J. Herrmann}
}
@conference {louboutin2023IMAGEloi,
	title = {Learned non-linear simultenous source and corresponding supershot for seismic imaging.},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2023},
	note = {(IMAGE, Houston)},
	month = {08},
	abstract = {Seismic imaging{\textquoteright}s main limiting factor is the scale of the involved dataset and the number of independent wave-equation solves required to migrate thousands of shots. To tackle this dimensionality curse, we introduce a learned framework that extends the conventional computationally reductive linear source superposition (e.g., via random simultaneous-source encoding) to a nonlinear learned source superposition and its corresponding learned supershot. With this method, we can image the subsurface at the cost of a one-shot migration by learning the most informative superposition of shots.},
	keywords = {deep learning, Imaging, SEG, simultaneous},
	url = {https://slimgroup.github.io/IMAGE2023/OneShot/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2023/louboutin2023IMAGEloi/louboutin2023IMAGEloi_pres.pdf},
	author = {Mathias Louboutin and Rafael Orozco and Ali Siahkoohi and Felix J. Herrmann}
}
@article {zhang2023otl,
	title = {Optimized time-lapse acquisition design via spectral gap ratio minimization},
	journal = {Geophysics},
	volume = {88},
	number = {4},
	year = {2023},
	note = {(Geophysics)},
	month = {07},
	pages = {A19-A23},
	abstract = {Modern-day reservoir management and monitoring of geological carbon storage increasingly call for costly time-lapse seismic data collection. In this letter, we show how techniques from graph theory can be used to optimize acquisition geometries for low-cost sparse 4D seismic. Based on midpoint-offset domain connectivity arguments, the proposed algorithm automatically produces sparse non-replicated time-lapse acquisition geometries that favor wavefield recovery.},
	keywords = {Acquisition, JRM, matrix factorization, spectral gap, survey design, time-lapse, wavefield reconstruction},
	doi = {10.1190/geo2023-0024.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2023/zhang2023otl/Spectral_Gap_Paper.html},
	author = {Yijun Zhang and Ziyi Yin and Oscar Lopez and Ali Siahkoohi and Mathias Louboutin and Rajiv Kumar and Felix J. Herrmann}
}
@conference {orozco2023AABIiter,
	title = {Refining Amortized Posterior Approximations using Gradient-Based Summary Statistics},
	booktitle = {5th Symposium on Advances in Approximate Bayesian Inference},
	year = {2023},
	note = {(AABI, Honolulu)},
	month = {06},
	abstract = {We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in maximally informative summary statistics. Amortized variational inference is restricted by the expressive power of the chosen variational distribution and the availability of training data in the form of joint data and parameter samples, which often lead to approximation errors such as the amortization gap. To address this issue, we propose an iterative framework that refines the current amortized posterior approximation at each step. Our approach involves alternating between two steps: (1) constructing a training dataset consisting of pairs of summarized data residuals and parameters, where the summarized data residual is generated using a gradient-based summary statistic, and (2) training a conditional generative model {\textendash} a normalizing flow in our examples {\textendash} on this dataset to obtain a probabilistic update of the unknown parameter. This procedure leads to iterative refinement of the amortized posterior approximations without the need for extra training data. We validate our method in a controlled setting by applying it to a stylized problem, and observe improved posterior approximations with each iteration. Additionally, we showcase the capability of our method in tackling realistically sized problems by applying it to transcranial ultrasound, a high-dimensional, nonlinear inverse problem governed by wave physics, and observe enhanced posterior quality through better image reconstruction with the posterior mean.},
	keywords = {AABI, Amortization Gap, Amortized Variational Inference, Bayesian inference, conditional normalizing flows, Summary Statistics},
	url = {https://arxiv.org/abs/2305.08733},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/AABI/2023/orozco2023AABIiter/aabi_poster.pdf},
	author = {Rafael Orozco and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@article {siahkoohi2022ravi,
	title = {Reliable amortized variational inference with physics-based latent distribution correction},
	journal = {Geophysics},
	volume = {88},
	number = {3},
	year = {2023},
	note = {(Geophysics)},
	month = {05},
	abstract = {Bayesian inference for high-dimensional inverse problems is challenged by the computational costs of the forward operator and the selection of an appropriate prior distribution. Amortized variational inference addresses these challenges where a neural network is trained to approximate the posterior distribution over existing pairs of model and data. When fed previously unseen data and normally distributed latent samples as input, the pretrained deep neural network{\textendash}-in our case a conditional normalizing flow{\textendash}-provides posterior samples with virtually no cost. However, the accuracy of this approach relies on the availability of high-fidelity training data, which seldom exists in geophysical inverse problems because of the highly heterogeneous structure of the Earth. In addition, accurate amortized variational inference requires the observed data to be drawn from the training data distribution. As such, we offer a solution that increases the resilience of amortized variational inference when faced with data distribution shifts, e.g., changes in the forward model or prior distribution. Our method involves a physics-based correction to the conditional normalizing flow latent distribution to provide a more accurate approximation to the posterior distribution for the observed data at hand. To accomplish this, instead of a standard Gaussian latent distribution, we parameterize the latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance. These unknown quantities are then estimated by minimizing the Kullback-Leibler divergence between the corrected and true posterior distributions. While generic and applicable to other inverse problems, by means of a seismic imaging example, we show that our correction step improves the robustness of amortized variational inference with respect to changes in number of source experiments, noise variance, and shifts in the prior distribution. This approach provides a seismic image with limited artifacts and an assessment of its uncertainty with approximately the same cost as five reverse-time migrations.},
	keywords = {Inverse problems, Normalizing flows, seismic imaging, Uncertainty quantification, Variational Inference},
	doi = {10.1190/geo2022-0472.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2023/siahkoohi2022ravi/paper.html},
	software = {https://github.com/slimgroup/ReliableAVI.jl},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@conference {yin2023EMIutm,
	title = {Uncertainty-aware time-lapse monitoring of geological carbon storage with learned surrogates},
	booktitle = {Engineering Mechanics Institute Conference},
	year = {2023},
	note = {(EMI, Atlanta)},
	month = {06},
	abstract = {Time-lapse seismic monitoring of CO2 sequestration is computationally expensive as it involves modeling of both fluid-flow physics and wave physics. It also requires differentiation through the solvers with respect to properties of interest in the subsurface. In this talk, we present a learned end-to-end inversion framework, which uses a pre-trained Fourier neural operator as a learned surrogate for the fluid-flow simulator in order to greatly reduces the cost associated with fluid-flow modeling and differentiation through the solver. Through synthetic experiments, we demonstrate the efficacy of this framework on inverting the subsurface permeability of the reservoir and on monitoring CO2 plumes. We further quantify the uncertainty of the permeability and CO2 plumes with conditional normalizing flow. With this framework, we can also forecast the growth of CO2 plumes in the future with uncertainty estimation without any acquired seismic data.},
	keywords = {amortized Bayes, conditional normalizing flows, deep learning, EMI, end-to-end, Fourier neural operators, GCS, inversion, machine learning, Normalizing flows, time-lapse, uncertain quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EMI/2023/yin2023EMIutm/yin2023EMIutm.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EMI/2023/yin2023EMIutm/index.html},
	author = {Ziyi Yin and Rafael Orozco and Mathias Louboutin and Ali Siahkoohi and Felix J. Herrmann}
}
@conference {louboutin2022RHPCafa,
	title = {Abstractions for at-scale seismic inversion},
	booktitle = {Rice Oil and Gas High Performance Computing Conference 2022},
	year = {2022},
	note = {Rice Oil and Gas High Performance Computing Conference 2022},
	month = {03},
	pages = {Thursday Workshop: Devito Training and Hackathon},
	abstract = {We present the SLIM open-source software framework for computational geophysics, and more generally, inverse problems based on the wave-equation (e.g., medical ultrasound). We developed a software environment aimed at scalable research and development by designing multiple layers of abstractions. This environment allows the researchers to easily formulate their problem in an abstract fashion, while still being able to exploit the latest developments in high-performance computing. We illustrate and demonstrate the benefits of our software design on many geophysical applications, including seismic inversion and physics-informed machine learning for geophysics (e.g., loop unrolled imaging, uncertainty quantification), all while facilitating the integration of external software.},
	keywords = {CCS, devito, FWI, HPC, inversion, JUDI, machine learning, RHPC, software, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/RHPC/2022/louboutin2022RHPCafa/RiceHPC22.pdf},
	url2 = {https://youtu.be/scRTbP8w6Wk?t=4542},
	author = {Mathias Louboutin and Ali Siahkoohi and Ziyi Yin and Rafael Orozco and Thomas J. Grady II and Yijun Zhang and Philipp A. Witte and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {louboutin2022SEGais,
	title = {Accelerating innovation with software abstractions for scalable computational geophysics},
	booktitle = {International Meeting for Applied Geoscience and Energy Expanded Abstracts},
	year = {2022},
	note = {(IMAGE, Houston)},
	month = {05},
	abstract = {We present the SLIM open-source software framework for computational geophysics, and more generally, inverse problems based on the wave-equation (e.g., medical ultrasound). We developed a software environment aimed at scalable research and development by designing multiple layers of abstractions. This environment allows the researchers to easily formulate their problem in an abstract fashion, while still being able to exploit the latest developments in high-performance computing. We illustrate and demonstrate the benefits of our software design on many geophysical applications, including seismic inversion and physics-informed machine learning for geophysics(e.g., loop unrolled imaging, uncertainty quantification), all while facilitating the integration of external software.},
	keywords = {CCS, devito, FWI, HPC, inversion, JUDI, machine learning, SEG, software, Uncertainty quantification},
	doi = {10.1190/image2022-3750561.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/louboutin2022SEGais/louboutin_seg22.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/louboutin2022SEGais/index.html},
	author = {Mathias Louboutin and Philipp A. Witte and Ali Siahkoohi and Gabrio Rizzuti and Ziyi Yin and Rafael Orozco and Felix J. Herrmann}
}
@presentation {orozco2022ML4SEISMICaos,
	title = {Adjoint operators as summary functions in amortized Bayesian inference frameworks},
	year = {2022},
	month = {11},
	abstract = {An important concern in seismic inverse problems is the large and varying size of observed data. The large size can cause computational cost concerns and its varying size (such as when changing receiver geometries) implies the need to rerun inference algorithms from scratch for each new observation. Motivated by these two problems, we take inspiration from the statistics literature which commonly relies on summary statistic of observed data. Summary statistic compress the observed data leaving only information needed for inference. In this work, we argue that the adjoint operator provides a natural candidate for a summary function in the context of physics-based inverse problems. We first mathematically show that for certain general assumptions transforming data under the adjoint operator defines a new conditional distribution which preserves the expectations of the original posterior. We validate our hypothesis by evaluating our framework in a learned amortized inference algorithm. Our seismic and medical synthetic experiments show computational gains and increased quality of point estimates using our framework. We discuss statistical metrics that show our learned posterior is well calibrated therefore justifying its use in uncertainty quantification.},
	keywords = {Amortized Inference, Bayesian inference, deep learning, Inverse problems, machine learning, medical imaging, ML4SEISMIC, Normalizing flows, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/orozco2022ML4SEISMICaos/index.html},
	author = {Rafael Orozco and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@presentation {yin2022ML4SEISMICavc,
	title = {Amortized velocity continuation with Fourier neural operators},
	year = {2022},
	month = {11},
	abstract = {Velocity continuation aims to map the migration image using one background model to the image using another background model. It is of great importance to quantify the uncertainty in seismic imaging result from various background models. With Fourier neural operators as a learned surrogate, this continuation from a given background model to an unseen background model can be quite accurately estimated with near-zero cost. However, the limitation of the prior art is that the input background model and the survey area are assumed to be fixed. The main contribution of this work is to extend the Fourier neural operator surrogate to be amortized over different given background models and survey areas. We verify the effectiveness of our learned surrogates by a realistic example on different areas of Parihaka dataset against different background models.},
	keywords = {Fourier neural operators, ML4SEISMIC, SLIM, Uncertainty quantification, velocity continuation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/yin2022ML4SEISMICavc/index.html},
	author = {Ali Siahkoohi and Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@conference {herrmann2022EAGEcvm,
	title = {Capturing velocity-model uncertainty and two-phase flow with Fourier Neural Operators},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2022},
	note = {(EAGE, Madrid)},
	month = {06},
	pages = {AI in Geoscience and Geophysics: Current Trends and Future Prospects (Dedicated Session)},
	keywords = {CCS, EAGE, Fourier neural operators, JRM, seismic imaging, Uncertainty quantification},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2022/herrmann2022EAGEcvm/index.html},
	author = {Ali Siahkoohi and Thomas J. Grady II and Abhinav Prakash Gahlot and Huseyin Tuna Erdinc and Felix J. Herrmann}
}
@article {siahkoohi2021dbif,
	title = {Deep Bayesian inference for seismic imaging with tasks},
	journal = {Geophysics},
	volume = {87},
	number = {5},
	year = {2022},
	note = {(Geophysics)},
	month = {07},
	pages = {281-302},
	abstract = {We propose to use techniques from Bayesian inference and deep neural networks to translate uncertainty in seismic imaging to uncertainty in tasks performed on the image, such as horizon tracking. Seismic imaging is an ill-posed inverse problem because of unavoidable bandwidth and aperture limitations, which that is hampered by the presence of noise and linearization errors. Many regularization methods, such as transform-domain sparsity promotion, have been designed to deal with the adverse effects of these errors, however, these methods run the risk of biasing the solution and do not provide information on uncertainty in the image space and how this uncertainty impacts certain tasks on the image. A systematic approach is proposed to translate uncertainty due to noise in the data to confidence intervals of automatically tracked horizons in the image. The uncertainty is characterized by a convolutional neural network (CNN) and to assess these uncertainties, samples are drawn from the posterior distribution of the CNN weights, used to parameterize the image. Compared to traditional priors, in the literature it is argued that these CNNs introduce a flexible inductive bias that is a surprisingly good fit for many diverse domains in imaging. The method of stochastic gradient Langevin dynamics is employed to sample from the posterior distribution. This method is designed to handle large scale Bayesian inference problems with computationally expensive forward operators as in seismic imaging. Aside from offering a robust alternative to maximum a posteriori estimate that is prone to overfitting, access to these samples allow us to translate uncertainty in the image, due to noise in the data, to uncertainty on the tracked horizons. For instance, it admits estimates for the pointwise standard deviation on the image and for confidence intervals on its automatically tracked horizons.},
	keywords = {deep priors, horizon tracking, seismic imaging, Uncertainty quantification},
	doi = {10.1190/geo2021-0666.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2022/siahkoohi2021dbif/paper.html},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@mastersthesis {siahkoohi2022THdgmf,
	title = {Deep generative models for solving geophysical inverse problems},
	year = {2022},
	note = {(PhD)},
	month = {07},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {My thesis presents several novel methods to facilitate solving large-scale inverse problems by utilizing recent advances in machine learning, and particularly deep generative modeling. Inverse problems involve reliably estimating unknown parameters of a physical model from indirect observed data that are noisy. Solving inverse problems presents primarily two challenges. The first challenge is to capture and incorporate prior knowledge into ill-posed inverse problems whose solutions cannot be uniquely identified. The second challenge is the computational complexity of solving inverse problems, particularly the cost of quantifying uncertainty. The main goal of this thesis is to address these issues by developing practical data-driven methods that are scalable to geophysical applications in which access to high-quality training data is often limited. There are six papers included in this thesis. A majority of these papers focus on addressing computational challenges associated with Bayesian inference and uncertainty quantification, while others focus on developing regularization techniques to improve inverse problem solution quality and accelerate the solution process. These papers demonstrate the applicability of the proposed methods to seismic imaging, a large-scale geophysical inverse problem with a computationally expensive forward operator for which sufficiently capturing the variability in the Earth{\textquoteright}s heterogeneous subsurface through a training dataset is challenging. The first two papers present computationally feasible methods of applying a class of methods commonly referred to as deep priors to seismic imaging and uncertainty quantification. I also present a systematic Bayesian approach to translate uncertainty in seismic imaging to uncertainty in downstream tasks performed on the image. The next two papers aim to address the reliability concerns surrounding data-driven methods for solving Bayesian inverse problems by leveraging variational inference formulations that offer the benefits of fully-learned posteriors while being directly informed by physics and data. The last two papers are concerned with correcting forward modeling errors where the first proposes an adversarially learned postprocessing step to attenuate numerical dispersion artifacts in wave-equation simulations due to coarse finite-difference discretizations, while the second trains a Fourier neural operator surrogate forward model in order to accelerate the qualification of uncertainty due to errors in the forward model parameterization.},
	keywords = {Bayesian inference, deep learning, Generative models, Geophysics, Inverse problems, PhD},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2022/siahkoohi2022THdgmf/siahkoohi2022THdgmf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2022/siahkoohi2022THdgmf/siahkoohi2022THdgmf_pres.pdf},
	author = {Ali Siahkoohi}
}
@presentation {yin2022TRANSFORMjulia,
	title = {Julia for Geoscience},
	year = {2022},
	month = {04},
	abstract = {In this tutorial, we will introduce the Julia programming language to the geoscience community, covering topics such as I/O, data processing, inversion, and machine learning. We will begin by installing Julia and relevant packages. Through a series of tutorials, we will demonstrate Julia{\textquoteright}s abstraction power and show how to load and plot data, write your own functions/operators, form and solve a geophysical inverse problem, and demonstrate how to integrate wave-equation solvers in Julia with machine learning frameworks. The intent of this presentation is to provide an introductory level tutorial that will be useful to members of the geoscience community.},
	keywords = {JOLI, JUDI, Julia, machine learning, SLIM, software, TRANSFORM},
	url = {https://transform.softwareunderground.org/2022-julia-for-geoscience},
	url2 = {https://www.youtube.com/watch?v=HyWfp3NzIbg},
	software = {https://github.com/slimgroup/SLIMTutorials},
	author = {Ziyi Yin and Mathias Louboutin and Philipp A. Witte and Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Henryk Modzelewski and Felix J. Herrmann}
}
@conference {yin2022SEGlci,
	title = {Learned coupled inversion for carbon sequestration monitoring and forecasting with Fourier neural operators},
	booktitle = {International Meeting for Applied Geoscience and Energy Expanded Abstracts},
	year = {2022},
	note = {(IMAGE, Houston)},
	month = {05},
	abstract = {Seismic monitoring of carbon storage sequestration is a challenging problem involving both fluid-flow physics and wave physics. Additionally, monitoring usually requires the solvers for these physics to be coupled and differentiable to effectively invert for the subsurface properties of interest. To drastically reduce the computational cost, we introduce a learned coupled inversion framework based on the wave modeling operator, rock property conversion and a proxy fluid-flow simulator. We show that we can accurately use a Fourier neural operator as a proxy for the fluid-flow simulator for a fraction of the computational cost. We demonstrate the efficacy of our proposed method by means of a synthetic experiment. Finally, our framework is extended to carbon sequestration forecasting, where we effectively use the surrogate Fourier neural operator to forecast the CO$_2$ plume in the future at near-zero additional cost.},
	keywords = {CCS, deep learning, Fourier neural operators, inversion, machine learning, multiphysics, SEG, time-lapse},
	doi = {10.1190/image2022-3722848.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/yin2022SEGlci/paper.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/yin2022SEGlci/index.html},
	software = {https://github.com/slimgroup/FNO4CO2},
	author = {Ziyi Yin and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {siahkoohi2022ML4SEISMICluq,
	title = {Low-cost uncertainty quantification for large-scale inverse problems},
	year = {2022},
	month = {11},
	abstract = {Bayesian inference for large-scale inverse problems is challenged by the computationally costly forward operator evaluations during posterior distribution sampling. Recent advances in variational inference and deep learning reduce these costs by pretraining a neural network capable of sampling the posterior distribution for previously unseen observed data. In geophysical applications, however, the accuracy of these methods depends on sufficiently capturing subsurface variability through a training dataset, which is challenging given the heterogeneity of the Earth{\textquoteright}s subsurface and our lack of access to it. Moreover, these methods may be unreliable in the presence of data distribution shifts, e.g., a change in the number of source experiments, noise distribution, or geological features to be imaged. As such, we present a solution that increases the robustness of deep-learning-based Bayesian inference approaches when faced with changes in data distribution. Our proposed method involves a physics-based adaptation to the latent distribution of a conditional normalizing flow that is pretrained to approximate the posterior distribution for previously unseen data. Instead of feeding standard Gaussian latent samples to the conditional normalizing flow, this method parameterizes the latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance, estimated by minimizing the Kullback-Leibler divergence between predicted and true posterior distributions. This method is applicable to a wide range of inverse problems and has the potential to significantly reduce the costs of Bayesian variational inference. By means of a realistic seismic imaging example we demonstrate that the proposed latent distribution adaptation method mitigates the Bayesian inference errors induced by data distribution shifts, including shifts in the forward model and prior distribution.},
	keywords = {Inverse problems, ML4SEISMIC, Normalizing flows, seismic imaging, SLIM, Uncertainty quantification, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/siahkoohi2022ML4SEISMICluq/siahkoohi2022ML4SEISMICluq_pres.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@conference {siahkoohi2022SEGWSrav,
	title = {Reliable amortized variational inference with conditional normalizing flows via physics-based latent distribution correction},
	booktitle = {IMAGE Workshop on Subsurface Uncertainty Description and Estimation - Moving Away from Single Prediction with Distribution Learning},
	year = {2022},
	note = {(IMAGE Workshop, Houston)},
	month = {09},
	abstract = {Bayesian inference for high-dimensional inverse problems is challenged by the computational costs associated with the forward operator during posterior sampling, as well as the selection of an appropriate prior distribution that encodes our prior knowledge about the unknown. Amortized variational inference addresses these challenges by pretraining a conditional normalizing flow (cNF) that approximates the posterior distribution over the existing model and data joint samples where the prior is implicitly learned from the data. When fed data and normally distributed latent samples as input, the pretrained cNF provides posterior samples for previously unseen data virtually for free. The accuracy of this purely data-driven approach, however, is dependent on the availability of high-fidelity training data, which is rarely the case with geophysical inverse problems, due to the highly heterogeneous structure of the Earth. To overcome this challenge and to minimize the negative bias of data distribution shifts during inference, we propose learning a physics-based correction to the cNF latent distribution to provide a more accurate approximation to the posterior distribution. We accomplish this by parameterizing the cNF latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance, which are estimated by minimizing the Kullback-Leibler divergence between the corrected posterior distribution estimate and the true posterior distribution. For a relatively well-trained cNF, this approach provides reliable posterior samples with a limited computational cost while remaining bound to data and physics. We showcase the computational gains of this approach on a "quasi" real seismic imaging example.},
	keywords = {Bayesian inference, deep learning, Generative models, Imaging, Inverse problems, SEG, Uncertainty quantification, workshop},
	url = {https://www.imageevent.org/Workshop/subsurface-uncertainty-description-estimation-moving-away-single-prediction-distribution-learning},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/siahkoohi2022SEGWSrav/Thur-15-55-Siahkoohi.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@conference {zhang2022SEGass,
	title = {A simulation-free seismic survey design by maximizing the spectral gap},
	booktitle = {International Meeting for Applied Geoscience and Energy Expanded Abstracts},
	year = {2022},
	note = {(IMAGE, Houston)},
	month = {05},
	abstract = {Due to the tremendous cost of seismic data acquisition, methods have been developed to reduce the amount of data acquired by designing optimal missing trace reconstruction algorithms. These technologies are designed to record as little data as possible in the field, while providing accurate wavefield reconstruction in the areas of the survey that are not recorded. This is achieved by designing randomized subsampling masks that allow for accurate wavefield reconstruction via matrix completion methods. Motivated by these recent results, we propose a simulation-free seismic survey design that aims at improving the quality of a given randomized subsampling using a simulated annealing algorithm that iteratively increases the spectral gap of the subsampling mask, a property recently linked to the quality of the reconstruction. We demonstrate that our proposed method improves the data reconstruction quality for a fixed subsampling rate on a realistic synthetic dataset.},
	keywords = {Acquisition, matrix factorization, SEG, spectral gap, survey design, wavefield reconstruction},
	doi = {10.1190/image2022-3751690.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/zhang2022SEGass/Yijun2022SEGass.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/zhang2022SEGass/index.html},
	software = {https://github.com/slimgroup/opt_spectral_gap},
	author = {Yijun Zhang and Mathias Louboutin and Ali Siahkoohi and Ziyi Yin and Rajiv Kumar and Felix J. Herrmann}
}
@presentation {zhang2022ML4SEISMICtss,
	title = {Time-lapse seismic survey design by maximizing the spectral gap},
	year = {2022},
	month = {11},
	abstract = {While time-lapse seismic has been applied successfully to CO2 sequestration monitoring, it remains a challenging problem since replicated dense surveys come at a very high cost in the field. Wavefield reconstruction based on matrix completion (MC) from randomized subsampled data is an efficient way to reduce operational costs. This technique allows for accurate time-lapse reconstruction by employing the joint recovery model (JRM), which capitalizes on the fact that different vintages share a common component. However, combining JRM with optimal time-lapse acquisition survey design remains an unexplored area of research. In expander graph theory, spectral gap (SG) reveals the source-receiver layout connectivity and is related to reconstruction quality during MC. Building on these insights, we proposed a simulation free time-lapse survey design based on JRM that aims to get similar reconstructed quality without insisting on replicate surveys, which significantly reduces the cost in the field. This approach uses the simulated annealing algorithm to find subsampling masks for each vintage. Numerical experiments confirm a direct correlation between increased spectral gap and promising time-lapse reconstruction quality.},
	keywords = {Acquisition, JRM, matrix factorization, ML4SEISMIC, SLIM, spectral gap, survey design, time-lapse, wavefield reconstruction},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/zhang2022ML4SEISMICtss/index.html},
	author = {Yijun Zhang and Mathias Louboutin and Ali Siahkoohi and Ziyi Yin and Rajiv Kumar and Oscar Lopez and Felix J. Herrmann}
}
@conference {siahkoohi2022INTERSPEECHulbs,
	title = {Ultra-Low-Bitrate Speech Coding with Pretrained Transformers},
	booktitle = {Proceedings of INTERSPEECH},
	year = {2022},
	note = {International Speech Communication Association (ISCA)},
	month = {06},
	abstract = {Speech coding facilitates the transmission of speech over low-bandwidth networks with minimal distortion. Neural-network based speech codecs have recently demonstrated significant improvements in quality over traditional approaches. While this new generation of codecs is capable of synthesizing high-fidelity speech, their use of recurrent or convolutional layers often restricts their effective receptive fields, which prevents them from compressing speech efficiently. We propose to further reduce the bitrate of neural speech codecs through the use of pretrained Transformers, capable of exploiting long-range dependencies in the input signal due to their inductive bias. As such, we use a pretrained Transformer in tandem with a convolutional encoder, which is trained end-to-end with a quantizer and a generative adversarial net decoder. Our numerical experiments show that supplementing the convolutional encoder of a neural speech codec with Transformer speech embeddings yields a speech codec with a bitrate of 600 bps that outperforms the original neural speech codec in synthesized speech quality when trained at the same bitrate. Subjective human evaluations suggest that the quality of the resulting codec is comparable or better than that of conventional codecs operating at three to four times the rate.},
	keywords = {deep learning, GANs, INTERSPEECH, signal processing, Transformers},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/INTERSPEECH/2022/siahkoohi2022INTERSPEECHulbs/paper.pdf},
	author = {Ali Siahkoohi and Michael Chinen and Tom Denton and W. Bastiaan Kleijn and Jan Skoglund}
}
@presentation {yin2022ML4SEISMICutc,
	title = {Uncertainty-aware time-lapse CO$_2$ monitoring with learned end-to-end inversion},
	year = {2022},
	month = {11},
	abstract = {Seismic monitoring of CO2 sequestration is computationally expensive as it involves modeling of both fluid-flow physics modeling and wave physics and differentiation through the solvers with respect to the subsurface properties of interest. In this talk, we demonstrate the effectiveness of learned coupled inversion framework using a pre-trained Fourier neural operator as a learned surrogate for the fluid-flow simulator, which greatly reduces the cost associated with fluid-flow modeling and differentiation through the solver. We study the effectiveness and correctness of inversion based on Fourier neural operator surrogate and a normalizing flow prior. We also demonstrate the efficacy of this framework on monitoring the growth of CO2 plumes during sequestration, and on uncertainty quantification of the permeability and CO2 plumes with conditional normalizing flow. With this framework, we can further forecast the CO2 plume in the future without any acquired seismic data with uncertainty estimation.},
	keywords = {amortized Bayes, conditional normalizing flows, deep learning, Fourier neural operators, GCS, inversion, machine learning, ML4SEISMIC, Normalizing flows, SLIM, time-lapse, uncertain quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/yin2022ML4SEISMICutc/index.html},
	author = {Ziyi Yin and Rafael Orozco and Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@conference {siahkoohi2022SEGvcw,
	title = {Velocity continuation with Fourier neural operators for accelerated uncertainty quantification},
	booktitle = {International Meeting for Applied Geoscience and Energy Expanded Abstracts},
	year = {2022},
	note = {(IMAGE, Houston)},
	month = {05},
	abstract = {Seismic imaging is an ill-posed inverse problem that is challenged by noisy data and modeling inaccuracies{\textendash}-due to errors in the background squared-slowness model. Uncertainty quantification is essential for determining how variability in the background models affects seismic imaging. Due to the costs associated with the forward Born modeling operator as well as the high dimensionality of seismic images, quantification of uncertainty is computationally expensive. As such, the main contribution of this work is a survey-specific Fourier neural operator surrogate to velocity continuation that maps seismic images associated with one background model to another virtually for free. While being trained with only 200 background and seismic image pairs, this surrogate is able to accurately predict seismic images associated with new background models, thus accelerating seismic imaging uncertainty quantification. We support our method with a realistic data example in which we quantify seismic imaging uncertainties using a Fourier neural operator surrogate, illustrating how variations in background models affect the position of reflectors in a seismic image.},
	keywords = {Fourier neural operators, SEG, Uncertainty quantification, velocity continuation},
	doi = {10.1190/image2022-3750475.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/siahkoohi2022SEGvcw/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2022/siahkoohi2022SEGvcw/Tue-16-30-Siahkoohi.pdf},
	software = {https://github.com/slimgroup/fno4vc},
	author = {Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@conference {siahkoohi2022EAGEweb,
	title = {Wave-equation based inversion with amortized variational Bayesian inference},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2022},
	note = {(EAGE, Madrid)},
	month = {06},
	pages = {Session 2: Velocity model building and imaging (different domains)},
	abstract = {Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth{\textquoteright}s highly heterogeneous structure is unknown, present a challenge in encoding prior knowledge through analytical expressions. Our main contribution is a generative-model-based regularization approach, robust to out-of-distribution data, which exploits the prior knowledge embedded in existing data and model pairs. Utilizing an amortized variational inference objective, a conditional normalizing flow (NF) is pretrained on pairs of low- and high-fidelity migrated images in order to achieve a low-fidelity approximation to the seismic imaging posterior distribution for previously unseen data. The NF is used after pretraining to reparameterize the unknown seismic image in an inversion scheme involving physics-guided data misfit and a Gaussian prior on the NF latent variable. Solving this optimization problem with respect to the latent variable enables us to leverage the benefits of data-driven conditional priors whilst being informed by physics and data. The numerical experiments demonstrate that the proposed inversion scheme produces seismic images with limited artifacts when dealing with noisy and out-of-distribution data.},
	keywords = {conditional priors, EAGE, Normalizing flows, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2022/siahkoohi2022EAGEweb/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2022/siahkoohi2022EAGEweb/Mon-Herrmann.pdf},
	software = {https://github.com/slimgroup/ConditionalNFs4Imaging.jl},
	author = {Ali Siahkoohi and Rafael Orozco and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {herrmann2021KAUSTdbi,
	title = {Deep Bayesian Inference for Task-based Seismic Imaging},
	booktitle = {KAUST},
	year = {2021},
	note = {(KAUST, virtual)},
	month = {03},
	abstract = {High dimensionality, complex physics, and lack of access to the ground truth make seismic imaging one of the most challenging inversion problems in the computational imaging sciences. If these challenges were not bad enough, modern applications of computational imaging increasingly call for the assessment of uncertainty on the image itself and on subsequent tasks conducted on these images. By making use of a Markov-chain Monte Carlo (McMC) sampling technique, we demonstrate how uncertainty in the data can be propagated to the task of seismic horizon tracking. While this example shows that uncertainty can in principle be handled in a systematic manner by using neural nets as deep priors, it unfortunately also reveals that the McMC method fundamentally lacks ability to scale to relevant problem sizes. To overcome this shortcoming, we introduce a variational formulation based on normalizing flows. In this approach, invertible neural networks are trained to generate samples from the posterior. There are strong indications that this approach has the capability to scale better to problems where the forward operator is expensive to evaluate.},
	keywords = {Bayesian inference, Inverse problems, seismic imaging, Uncertainty quantification},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/KAUST/2021/herrmann2021KAUSTdbi/Kaust.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Mathias Louboutin and Philipp A. Witte and Felix J. Herrmann}
}
@conference {kumar2021SEGeuq,
	title = {Enabling uncertainty quantification for seismic data pre-processing using normalizing flows (NF){\textemdash}an interpolation example},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2021},
	note = {(IMAGE, Denver)},
	month = {09},
	pages = {1515-1519},
	abstract = {Seismic data go through a sequence of pre-processing steps before being made into an image. Although some work has been done to assess the uncertainties in the final images, how the uncertainty in the pre-processing affects the results remains largely unexplored. We use Normalizing Flows (NF), a type of deep neural network, to interpolate seismic data and quantify the associated uncertainty. A big advantage of NFs, over the more commonly used Markov Chain Monte Carlo methods, is that they can successfully sample a complex and high-dimensional probability space with fewer assumptions. We present the first application of NF in interpolating (synthetic) seismic data. The statistical measurements retrieved from the network can be used to better characterize the data as it is passed to the post-processing phase.},
	keywords = {deep learning, normalizing flow, SEG, wavefield reconstruction},
	doi = {10.1190/segam2021-3583705.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/kumar2021SEGeuq/kumar2021SEGeuq.pdf},
	software = {https://github.com/slimgroup/Software.SEG2021},
	author = {Rajiv Kumar and Maria Kotsi and Ali Siahkoohi and Alison Malcolm}
}
@conference {siahkoohi2021EarthMLfar,
	title = {Fast and reliability-aware seismic imaging with conditional normalizing flows},
	booktitle = {Intelligent illumination of the Earth},
	year = {2021},
	note = {(KAUST, virtual)},
	month = {09},
	abstract = {The posterior probability distribution provides a comprehensive description of the solution in ill-posed inverse problems. Sampling from the posterior distribution in the context of seismic imaging is challenged by the high-dimensionality of the unknown and the expensive-to-evaluate forward operator. These challenges limit the applicability of Markov Chain sampling methods due to the costs associated with the forward operator. Moreover, explicitly choosing a prior distribution that captures the true heterogeneity exhibited by the Earth{\textquoteright}s subsurface further complicates casting seismic imaging into a Bayesian framework. To handle this situation and to assess uncertainty, we propose a data-driven variational inference approach based on conditional normalizing flows (NFs). The proposed scheme leverages existing data, which are in the form of low- and high-fidelity migrated image pairs, to train a conditional NF capable of characterizing the posterior distribution. After training, the NF can be used to sample from the posterior distribution associated with a previously unseen seismic survey, which is in some sense close, e.g., data from a neighboring survey area. In our numerical example, we obtain high-fidelity images from the Parihaka dataset and low-fidelity images are derived from these images through the process of demigration, followed by adding band-limited noise and migration. During inference, given shot records from a new neighboring seismic survey, we first compute the reverse-time migration image. Next, by feeding this low-fidelity migrated image to the NF we gain access to samples from the posterior distribution virtually for free. We use these samples to compute a high-fidelity image including a first assessment of the image{\textquoteright}s reliability.},
	keywords = {Normalizing flows, seismic imaging, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/KAUST/2021/siahkoohi2021EarthMLfar/siahkoohi2021EarthMLfar.pdf},
	author = {Ali Siahkoohi and Rafael Orozco and Gabrio Rizzuti and Philipp A. Witte and Mathias Louboutin and Felix J. Herrmann}
}
@conference {witte2021JULIACONmedlj,
	title = {InvertibleNetworks.jl - Memory efficient deep learning in Julia},
	booktitle = {JuliaCon},
	year = {2021},
	note = {(JuliaCon, virtual)},
	month = {07},
	abstract = {We present InvertibleNetworks.jl, an open-source package for invertible neural networks and normalizing flows using memory-efficient backpropagation. InvertibleNetworks.jl uses manually implement gradients to take advantage of the invertibility of building blocks, which allows for scaling to large-scale problem sizes. We present the architecture and features of the library and demonstrate its application to a variety of problems ranging from loop unrolling to uncertainty quantification.},
	keywords = {deep learning, Invertible network, Julia, Normalizing flows, segmentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/JuliaCon/2021/witte2021JULIACONmedlj/witte2021JULIACONmedlj.pdf},
	url2 = {https://www.youtube.com/watch?v=9M-zEGHY4i4},
	author = {Philipp A. Witte and Mathias Louboutin and Ali Siahkoohi and Gabrio Rizzuti and Bas Peters and Felix J. Herrmann}
}
@conference {herrmann2021Delftlwi,
	title = {Learned wave-based imaging - variational inference at scale},
	booktitle = {Delft},
	year = {2021},
	note = {(Delft, virtual)},
	month = {06},
	abstract = {High dimensionality, complex physics, and lack of access to the ground truth rank medical ultrasound and seismic imaging amongst the most challenging problems in the computational imaging sciences. If these challenges were not bad enough, modern applications of computational imaging increasingly call for the assessment of uncertainty on the image itself and on subsequent tasks. During this talk, I will show how recent developments in Normalizing Flows, a new type of invertible neural networks, can be used to cast wave-based imaging into a scalable Bayesian framework. Contrary to conventional methods, where sample images are drawn from the posterior distribution during inversion, our approach trains Normalizing Flows capable of generating samples from the posterior. Aside from greatly reducing the computational cost, this approach gives us access to the image itself (via Maximum a posteriori or mean estimation) and its multidimensional statistical distribution including its pointwise variance.},
	keywords = {medical imaging, Normalizing flows, seismic imaging, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/Delft/2021/herrmann2021Delftlwi/herrmann2021Delftlwi.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/Delft/2021/herrmann2021Delftlwi/herrmann2021Delftlwi.mp4},
	author = {Felix J. Herrmann and Ali Siahkoohi and Rafael Orozco and Gabrio Rizzuti and Philipp A. Witte and Mathias Louboutin}
}
@conference {siahkoohi2021SEGlbe,
	title = {Learning by example: fast reliability-aware seismic imaging with normalizing flows},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2021},
	note = {(IMAGE, Denver)},
	month = {09},
	pages = {1580-1585},
	abstract = {Uncertainty quantification provides quantitative measures on the reliability of candidate solutions of ill-posed inverse problems. Due to their sequential nature, Monte Carlo sampling methods require large numbers of sampling steps for accurate Bayesian inference and are often computationally infeasible for large-scale inverse problems, such as seismic imaging. Our main contribution is a data-driven variational inference approach where we train a normalizing flow (NF), a type of invertible neural net, capable of cheaply sampling the posterior distribution given previously unseen seismic data from neighboring surveys. To arrive at this result, we train the NF on pairs of low- and high-fidelity migrated images. In our numerical example, we obtain high-fidelity images from the Parihaka dataset and low-fidelity images are derived from these images through the process of demigration, followed by adding noise and migration. During inference, given shot records from a new neighboring seismic survey, we first compute the reverse-time migration image. Next, by feeding this low-fidelity migrated image to the NF we gain access to samples from the posterior distribution virtually for free. We use these samples to compute a high-fidelity image including a first assessment of the image{\textquoteright}s reliability. To our knowledge, this is the first attempt to train a conditional network on what we know from neighboring images to improve the current and assess its reliability.},
	keywords = {deep learning, Normalizing flows, SEG, seismic imaging, Variational Inference},
	doi = {10.1190/segam2021-3581836.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/siahkoohi2021SEGlbe/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/siahkoohi2021SEGlbe/Tue-09-15-siahkoohi.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/siahkoohi2021SEGlbe/Tue-09-15-siahkoohi.mp4},
	software = {https://github.com/slimgroup/Software.SEG2021},
	author = {Ali Siahkoohi and Felix J. Herrmann}
}
@techreport {louboutin2021NIPSmcte,
	title = {Low-memory stochastic backpropagation with multi-channel randomized trace estimation},
	number = {TR-CSE-2021-1},
	year = {2021},
	month = {06},
	abstract = {Thanks to the combination of state-of-the-art accelerators and highly optimized open software frameworks, there has been tremendous progress in the performance of deep neural networks. While these developments have been responsible for many breakthroughs, progress towards solving large-scale problems, such as video encoding and semantic segmentation in 3D, is hampered because access to on-premise memory is often limited. Instead of relying on (optimal) checkpointing or invertibility of the network layers{\textendash}-to recover the activations during backpropagation{\textendash}-we propose to approximate the gradient of convolutional layers in neural networks with a multi-channel randomized trace estimation technique. Compared to other methods, this approach is simple, amenable to analyses, and leads to a greatly reduced memory footprint. Even though the randomized trace estimation introduces stochasticity during training, we argue that this is of little consequence as long as the induced errors are of the same order as errors in the gradient due to the use of stochastic gradient descent. We discuss the performance of networks trained with stochastic backpropagation and how the error can be controlled while maximizing memory usage and minimizing computational overhead.},
	keywords = {Convolutions, HPC, Low Memory, machine learning, randomized linear algebra},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2021/louboutin2021NIPSmcte/louboutin2021NIPSmcte.pdf},
	software = {https://github.com/slimgroup/XConv},
	author = {Mathias Louboutin and Ali Siahkoohi and Rongrong Wang and Felix J. Herrmann}
}
@conference {herrmann2021Microsoftrla,
	title = {ML@scale using randomized linear algebra},
	booktitle = {Microsoft},
	year = {2021},
	note = {Talk at Microsoft},
	month = {03},
	abstract = {Deep Learning for large-scale applications such as video encoding or seismic segmentation are challenged by the excessive amounts of memory that is required for training networks via backpropagation. In this talk, I will discuss how techniques from randomized linear algebra can be used to address these bottle necks and bring down the memory footprint of training CNNs by up to a factor of O(N) (where N is number of pixels) without increasing computational cost. Additionally, I will illustrate how the seemingly disparate technologies of deep learning and large-scale PDE-constrained optimization share important similarities that can be taken advantage of in the development of next-generation deep learning technologies, with possible applications in scientific computing and sustainability.},
	keywords = {deep learning, randomized linear algebra, Uncertainty quantification},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/Microsoft/2021/herrmann2021Microsoftrla/herrmann2021Microsoftrla_pres.pdf},
	author = {Felix J. Herrmann and Mathias Louboutin and Ali Siahkoohi}
}
@presentation {siahkoohi2021ML4SEISMICmcn,
	title = {Multifidelity conditional normalizing flows for physics-guided Bayesian inference},
	year = {2021},
	month = {11},
	abstract = {We introduce a scalable Bayesian inference approach that combines techniques from deep learning with a physic-based variational inference formulation. Bayesian inference for ill-posed inverse problems is challenged by the high-dimensionality of the unknown, computationally expensive forward operator, and choosing a prior distribution that accurately encodes prior knowledge on the unknown. To handle this situation and to assess uncertainty, we propose to approximate the posterior distribution using a pretrained conditional normalizing flow, which is trained on existing low- and high-fidelity estimations of the unknown. To further improve the accuracy of this approximation, we use transfer learning and finetune this normalizing flow by minimizing the Kullback-Leibler divergence between the predicted and the desired high-fidelity posterior density. This amounts to minimizing a physic-based variational inference objective with respect to the network weights, which we believe might scale better than Bayesian inference with Markov Chain sampling methods. We apply the proposed Bayesian inference approach to seismic imaging where we use quasi-real data obtained from the Parihaka dataset.},
	keywords = {deep learning, ML4SEISMIC, Normalizing flows, seismic imaging, SLIM, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/siahkoohi2021ML4SEISMICmcn/Mon-11-45-Siahkoohi.pdf},
	author = {Ali Siahkoohi and Rafael Orozco and Gabrio Rizzuti and Philipp A. Witte and Mathias Louboutin and Felix J. Herrmann}
}
@conference {orozco2021NIPSpicp,
	title = {Photoacoustic Imaging with Conditional Priors from Normalizing Flows},
	booktitle = {Neural Information Processing Systems (NeurIPS)},
	year = {2021},
	note = {(NIPS, virtual)},
	month = {12},
	abstract = {Photoacoustic imaging is a biomedical imaging technique based on the photoacoustic effect. It leverages the interplay between optics and acoustics as a mean to circumvent the limitations of imaging modalities relying on single-type physics. Light beams generated by a pulsed laser can penetrate biological tissues by several centimeters, and are absorbed based on oxygen saturation or hemoglobin concentration. While optical absorption is in principle an ideal parameter for medical imaging (e.g., with respect to the detection of cancerous tissue), strong scattering imposes important limitations in its imaging resolution. Ultrasonics, on the other hand, can theoretically provide resolution of medical diagnostic value, but produce images of mechanical properties whose contrasts are not sensitive. In photoacoustics, optical and acoustic effects are combined to gain the best of both worlds. Under conditions of thermal and stress confinement, thermal energy can efficiently build up in biological tissues, which in turn undergo thermal expansion and effectively act as a spatially distributed acoustic source. In photoacoustic imaging, the actual object of interest is the induced source, as it is directly related to optical absorption and can be recovered with a relatively higher resolution than pure optical imaging, based on the acquired ultrasonic data.},
	keywords = {conditional prior, deep image, MAP, NIPS, normalizing flow, Photoacoustic, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2021/orozco2021NIPSpicp/deep_inverse_2021.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2021/orozco2021NIPSpicp/posterneurips2021_orozco.pdf},
	url2 = {https://openreview.net/forum?id=woi1OTvROO1},
	software = {https://github.com/slimgroup/InvertibleNetworks.jl},
	author = {Rafael Orozco and Ali Siahkoohi and Gabrio Rizzuti and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {siahkoohi2021AABIpto,
	title = {Preconditioned training of normalizing flows for variational inference in inverse problems},
	booktitle = {3rd Symposium on Advances in Approximate Bayesian Inference},
	year = {2021},
	note = {AABI},
	month = {01},
	abstract = {Obtaining samples from the posterior distribution of inverse problems with expensive forward operators is challenging especially when the unknowns involve the strongly heterogeneous Earth. To meet these challenges, we propose a preconditioning scheme involving a conditional normalizing flow (NF) capable of sampling from a low-fidelity posterior distribution directly. This conditional NF is used to speed up the training of the high-fidelity objective involving minimization of the Kullback-Leibler divergence between the predicted and the desired high-fidelity posterior density for indirect measurements at hand. To minimize costs associated with the forward operator, we initialize the high-fidelity NF with the weights of the pretrained low-fidelity NF, which is trained beforehand on available model and data pairs. Our numerical experiments, including a 2D toy and a seismic compressed sensing example, demonstrate that thanks to the preconditioning considerable speed-ups are achievable compared to training NFs from scratch.},
	keywords = {Inverse problems, Normalizing flows, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/AABI/2021/siahkoohi2021AABIpto/siahkoohi2020ABIfab.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/AABI/2021/siahkoohi2021AABIpto/siahkoohi2021AABIpto_pres.pdf},
	url2 = {https://openreview.net/forum?id=P9m1sMaNQ8T},
	software = {https://github.com/slimgroup/Software.siahkoohi2021AABIpto},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Mathias Louboutin and Philipp A. Witte and Felix J. Herrmann}
}
@conference {ren2021AGUsvi,
	title = {Seismic Velocity Inversion and Uncertainty Quantification Using Conditional Normalizing Flows},
	booktitle = {AGU Annual Meeting},
	year = {2021},
	note = {(AGU 2021, New Orleans)},
	month = {12},
	pages = {U12A-03},
	abstract = {In this work, we use a conditional normalizing flow (CNF) to address the seismic velocity inversion problem. Considering the large dimension difference between seismic data and velocity model, we reduce the data dimension by calculating its reverse time. After that, we train the CNF on pairs of migrated data and velocity. During inference, given a new seismic data, feeding the corresponding migrated image into the trained CNF will lead to posterior samples of the velocity inversion distribution. In addition, uncertainty quantification of the inverted results can be achieved by statistical metrics like mean and standard deviation. In our numerical example, the implementation is based on open-sourced software InvertibleNetworks.jl (Witte et al., 2021), JUDI.jl (Witte et al., 2019) and Devito (Louboutin et al., 2019). The training dataset are built based on the SEG/EAGE Overthrust model. For an unseen seismic data, the posterior samples of inversion results given by the trained CNF can be considered as good estimates of the true velocity. Especially, judging from the metrics like MAE, MSE, PSNR, SSIM, et al., the posterior mean is usually closer to the true velocity and the standard deviation indicates that the velocity value is more reliable within the subsurface layers than that on layer edges. Moreover, the inverted results, either the posterior samples or posterior mean, can be used as an initial model in the subsequent FWI for a more accurate result.},
	keywords = {AGU, inversion, machine learning, Normalizing flows, Uncertainty quantification},
	url = {https://agu.confex.com/agu/fm21/meetingapp.cgi/Paper/815883},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/AGU/2021/ren2021AGUsvi/ren2021AGUsvi_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/AGU/2021/ren2021AGUsvi/ren2021AGUsvi.mp4},
	software = {https://github.com/slimgroup/INN_Velocity-Migration},
	author = {Yuxiao Ren and Philipp A. Witte and Ali Siahkoohi and Mathias Louboutin and Ziyi Yin and Felix J. Herrmann}
}
@article {sanavi2021tad,
	title = {True amplitude depth migration using curvelets},
	journal = {Geophysics},
	volume = {86},
	number = {4},
	year = {2021},
	note = {(Geophysics)},
	month = {07},
	pages = {S299-S310},
	abstract = {We have developed a true amplitude solution to the seismic imaging problem. We derive a diagonal scaling approach for the normal operator approximation in the curvelet domain. This is based on the theorem that states that curvelets remain approximately invariant under the action of the normal operator. We use curvelets as essential tools for approximation and inversion. We also exploit the theorem that states that the curvelet-domain approximation should be smooth in phase space by enforcing the smoothness of curvelet coefficients in the angle and space domains. We analyze our method using a reverse time migration-demigration code, simulating the acoustic wave equation on different synthetic models. Our method produces a good resolution with reflecting dips, reproduces the true amplitude reflectors, and compensates for incomplete illumination in seismic images.},
	keywords = {amplitude, depth migration, Imaging, inversion, LSRTM},
	doi = {10.1190/geo2019-0307.1},
	author = {Hamideh Sanavi and Peyman P. Moghaddam and Felix J. Herrmann}
}
@presentation {siahkoohi2021ML4SEISMICuqi,
	title = {Uncertainty quantification in imaging and automatic horizon tracking{\textemdash}a Bayesian deep-prior based approach},
	year = {2021},
	month = {11},
	abstract = {In inverse problems, uncertainty quantification (UQ) deals with a probabilistic description of the solution nonuniqueness and data noise sensitivity. Setting seismic imaging into a Bayesian framework allows for a principled way of studying uncertainty by solving for the model posterior distribution. Imaging, however, typically constitutes only the first stage of a sequential workflow, and UQ becomes even more relevant when applied to subsequent tasks that are highly sensitive to the inversion outcome. In this paper, we focus on how UQ trickles down to horizon tracking for the determination of stratigraphic models and investigate its sensitivity with respect to the imaging result. As such, the main contribution of this work consists in a data-guided approach to horizon tracking uncertainty analysis. This work is fundamentally based on a special reparameterization of reflectivity, known as {\textquotedblleft}deep prior{\textquotedblright}. Feasible models are restricted to the output of a convolutional neural network with a fixed input, while weights and biases are Gaussian random variables. Given a deep prior model, the network parameters are sampled from the posterior distribution via a Markov chain Monte Carlo method, from which the conditional mean and point-wise standard deviation of the inferred reflectivities are approximated. For each sample of the posterior distribution, a reflectivity is generated, and the horizons are tracked automatically. In this way, uncertainty on model parameters naturally translates to horizon tracking. As part of the validation for the proposed approach, we verified that the estimated confidence intervals for the horizon tracking coincide with geologically complex regions, such as faults.},
	keywords = {horizon picking, Imaging, machine learning, ML4SEISMIC, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/siahkoohi2021ML4SEISMICuqi/Mon-11-20-Siahkoohi.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@presentation {orozco2021ML4SEISMICvia,
	title = {Variational inference for artifact removal of adjoint solutions in photoacoustic problems},
	year = {2021},
	month = {11},
	abstract = {Photoacoustic is a medical imaging modality which combines light and ultrasound waves to image internal structures of biological tissue. The inverse problem reconstructs the tissue initially excited by light given propagated ultrasound data at receivers outside the tissue. Due to noisy, limited-view and sparse receiver data, traditional time-reversal adjoint solutions are highly ill-posed. This necessitates uncertainty quantification to communicate to practitioners which areas of the image can be trusted. We propose a framework which leverages a machine learning based method (Conditional Normalizing Flows) to learn the full posterior distribution of viable solutions given the time-reversal adjoint solution. We show that areas of calculated uncertainty correlate with structures that are known to be difficult to image. In addition, we also propose a MAP based solution, which solves the variational least-squares problem while using the trained Conditional Normalizing Flow as a prior distribution.},
	keywords = {conditional prior, deep image, MAP, ML4SEISMIC, normalizing flow, Photoacoustic, SLIM, Variational Inference},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/orozco2021ML4SEISMICvia/Tue-09-00-Orozco.html},
	author = {Rafael Orozco and Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {siahkoohi2020EAGEdlb,
	title = {A deep-learning based Bayesian approach to seismic imaging and uncertainty quantification},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2020},
	note = {Accepted in EAGE},
	month = {1},
	abstract = {Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is via formulating the posterior distribution. Unfortunately, it is often not possible to formulate a prior distribution that precisely encodes our prior knowledge about the unknown. Furthermore, adherence to handcrafted priors may greatly bias the outcome of the Bayesian analysis. To address this issue, we propose to use the functional form of a randomly initialized convolutional neural network as an implicit structured prior, which is shown to promote natural images and excludes images with unnatural noise. In order to incorporate the model uncertainty into the final estimate, we sample the posterior distribution using stochastic gradient Langevin dynamics and perform Bayesian model averaging on the obtained samples. Our synthetic numerical experiment verifies that deep priors combined with Bayesian model averaging are able to partially circumvent imaging artifacts and reduce the risk of overfitting in the presence of extreme noise. Finally, we present pointwise variance of the estimates as a measure of uncertainty, which coincides with regions that are difficult to image.},
	keywords = {deep learning, EAGE, seismic imaging, stochastic gradient Langevin dynamics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2020/siahkoohi2020EAGEdlb/siahkoohi2020EAGEdlb.html},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@presentation {siahkoohi2020SEGCHAPTERGTdlbuq,
	title = {A deep-learning based Bayesian approach to seismic imaging and uncertainty quantification},
	year = {2020},
	note = {(SEG Student Chapter)},
	abstract = {Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is via formulating the posterior distribution. Unfortunately, it is often not possible to formulate a prior distribution that precisely encodes our prior knowledge about the unknown. Furthermore, adherence to handcrafted priors may greatly bias the outcome of the Bayesian analysis. To address this issue, we propose to use the functional form of a randomly initialized convolutional neural network as an implicit structured prior, which is shown to promote natural images and excludes images with unnatural noise. In order to incorporate the model uncertainty into the final estimate, we sample the posterior distribution using stochastic gradient Langevin dynamics and perform Bayesian model averaging on the obtained samples. Our synthetic numerical experiment verifies that deep priors combined with Bayesian model averaging are able to partially circumvent imaging artifacts and reduce the risk of overfitting in the presence of extreme noise. Finally, we present pointwise variance of the estimates as a measure of uncertainty, which coincides with regions that are more difficult to image.},
	keywords = {deep learning, seismic imaging, stochastic gradient Langevin dynamics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Lectures/SEGCHAPTERGT/2020/siahkoohi2020SEGCHAPTERGTdlbuq/siahkoohi2020SEGCHAPTERGTdlbuq.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@article {witte2019TPDedas,
	title = {An Event-Driven Approach to Serverless Seismic Imaging in the Cloud},
	journal = {IEEE Transactions on Parallel and Distributed Systems},
	volume = {31},
	number = {9},
	year = {2020},
	note = {(IEEE Transactions on Parallel and Distributed Systems)},
	month = {03},
	pages = {2032-2049},
	abstract = {Adapting the cloud for high-performance computing (HPC) is a challenging task, as software for HPC applications hinges on fast network connections and is sensitive to hardware failures. Using cloud infrastructure to recreate conventional HPC clusters is therefore in many cases an infeasible solution for migrating HPC applications to the cloud. As an alternative to the generic lift and shift approach, we consider the specific application of seismic imaging and demonstrate a serverless and event-driven pproach for running large-scale instances of this problem in the cloud. Instead of permanently running compute instances, our workflow is based on a serverless architecture with high throughput batch computing and event-driven computations, in which computational resources are only running as long as they are utilized. We demonstrate that this approach is very flexible and allows for resilient and nested levels of parallelization, including domain decomposition for solving the underlying partial differential equations. While the event-driven approach introduces some overhead as computational resources are repeatedly restarted, it inherently provides resilience to instance shut-downs and allows a significant reduction of cost by avoiding idle instances, thus making the cloud a viable alternative to on-premise clusters for large-scale seismic imaging.},
	keywords = {cloud, event-driven, Imaging, LSRTM, serverless},
	doi = {10.1109/TPDS.2020.2982626},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETPDS/2020/witte2019TPDedas/witte2019TPDedas.html},
	author = {Philipp A. Witte and Mathias Louboutin and Henryk Modzelewski and Charles Jones and James Selvage and Felix J. Herrmann}
}
@techreport {siahkoohi2020TRfuqf,
	title = {Faster Uncertainty Quantification for Inverse Problems with Conditional Normalizing Flows},
	number = {TR-CSE-2020-2},
	year = {2020},
	month = {07},
	institution = {Georgia Institute of Technology},
	abstract = {In inverse problems, we often have access to data consisting of paired samples $(x,y)\sim p_X,Y(x,y)$ where $y$ are partial observations of a physical system, and $x$ represents the unknowns of the problem. Under these circumstances, we can employ supervised training to learn a solution $x$ and its uncertainty from the observations $y$. We refer to this problem as the "supervised" case. However, the data $y\sim p_Y(y)$ collected at one point could be distributed differently than observations $y{\textquoteright}\sim p_Y{\textquoteright}(y{\textquoteright})$, relevant for a current set of problems. In the context of Bayesian inference, we propose a two-step scheme, which makes use of normalizing flows and joint data to train a conditional generator $q_θ(x|y)$ to approximate the target posterior density $p_X|Y(x|y)$. Additionally, this preliminary phase provides a density function $q_θ(x|y)$, which can be recast as a prior for the "unsupervised" problem, e.g. when only the observations $y{\textquoteright}\sim p_Y{\textquoteright}(y{\textquoteright})$, a likelihood model $y{\textquoteright}|x$, and a prior on $x{\textquoteright}$ are known. We then train another invertible generator with output density $q{\textquoteright}_φ(x|y{\textquoteright})$ specifically for $y{\textquoteright}$, allowing us to sample from the posterior $p_X|Y{\textquoteright}(x|y{\textquoteright})$. We present some synthetic results that demonstrate considerable training speedup when reusing the pretrained network $q_θ(x|y{\textquoteright})$ as a warm start or preconditioning for approximating $p_X|Y{\textquoteright}(x|y{\textquoteright})$, instead of learning from scratch. This training modality can be interpreted as an instance of transfer learning. This result is particularly relevant for large-scale inverse problems that employ expensive numerical simulations.},
	keywords = {deep learning, invertible networks, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2020/siahkoohi2020TRfuqf/siahkoohi2020TRfuqf.html},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Philipp A. Witte and Felix J. Herrmann}
}
@mastersthesis {sharan2020THlsh,
	title = {Large scale high-frequency seismic wavefield reconstruction, acquisition via rank minimization and sparsity-promoting source estimation},
	year = {2020},
	note = {(PhD)},
	month = {11},
	school = {Georgia Institute of Technology},
	type = {phd},
	address = {Atlanta},
	abstract = {Seismic data reconstruction on a dense periodic grid from seismic data acquired on a coarse grid is a common approach followed by most of the oil \& gas companies. This approach allows them to save on operationally challenging and expensive dense seismic data acquisition. Dense seismic data is one of the key requirements for generating high-resolution images of earth{\textquoteright}s subsurface for exploration and production decisions. Based on the Compressive Sensing (CS) paradigm, low-rank matrix factorization based seismic data reconstruction methods are computationally cheaper and scalable to large datasets in comparison to sparsity-promotion based methods. The sparsity-promotion based methods are based on transformation in certain transform domains that can be computationally expensive for large datasets. Although, low-rank matrix factorization based methods perform well at lower frequencies, their performance degrades at higher frequencies due to increase in rank of approximating matrix. One of the contributions of this thesis is a recursively weighted matrix factorization approach to improve the quality of reconstructed data at higher frequencies. This recursively weighted approach exploits the similarity between adjacent frequency slices. Although, recursively weighted method improves the data reconstruction quality at higher frequencies, it can be computationally expensive for large scale seismic datasets. This is because of the interdependence of frequencies preventing simultaneous reconstruction of frequencies. Another contribution of this thesis is a computationally efficient recursively weighted framework for large scale dataset by parallelizing data reconstruction over rows of low-rank factors of each frequency slices. To reduce the cost and turnaround time of seismic data acquisition simultaneous source acquisition is adapted by the oil and gas industry in last few years. Another contribution of this thesis is a low-rank based method for simultaneous separation and reconstruction of seismic data on a dense periodic grid from large scale seismic data acquired with simultaneous source acquisition. Next part of this thesis focuses on accurate detection of fractures created by hydraulic fracturing in unconventional reservoirs for economical production of oil and gas. Fracturing of rocks during hydraulic fracturing gives rise to microseismic events, which are localized along these fractures. In this work, a sparsity-promoting microseismic source estimation framework is proposed to detect closely spaced microseismic sources along with estimation of their associated source-time functions from noisy microseismic data recorded by receivers along the earth{\textquoteright}s surface or along monitor wells. Detecting closely spaced microseismic events helps in delineating fractures and estimation of source-time function is useful in estimating fracture{\textquoteright}s origin in time. Also, source-time functions can be potentially useful for estimating the source-mechanism. Also, this method does not make any prior assumption on number of microseismic sources or shape of their source-time functions. Therefore, this method is useful for detecting microseismic sources with different source signatures and frequency content. Last part of this thesis focuses on sparsity-promoting photoacoustic imaging to detect photoabsorbers along with estimating the associated source-time functions. Traditional photoacoustic imaging can only estimate the locations of photoacoustic absorbers. Also, traditional methods require dense transducer coverage whereas sparsity-promotion based method can work with reduced transducer sampling reducing the overall data storage cost.},
	keywords = {compressed sensing, low-rank, PhD, Sparsity-promoting, wavefield reconstruction},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2020/sharan2020THlsh/sharan2020THlsh.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2020/sharan2020THlsh/sharan2020THlsh_pres.pdf},
	author = {Shashin Sharan}
}
@techreport {sharan2020lsh,
	title = {Large scale high-frequency wavefield reconstruction with recursively weighted matrix factorizations},
	number = {TR-CSE-2020-4},
	year = {2020},
	month = {10},
	abstract = {Acquiring seismic data on a regular periodic fine grid is challenging. By exploiting the low-rank approximation property of fully sampled seismic data in some transform domain, low-rank matrix completion offers a scalable way to reconstruct seismic data on a regular periodic fine grid from coarsely randomly sampled data acquired in the field. While wavefield reconstruction have been applied successfully at the lower end of the spectrum, its performance deteriorates at the higher frequencies where the low-rank assumption no longer holds rendering this type of wavefield reconstruction ineffective in situations where high resolution images are desired. We overcome this shortcoming by exploiting similarities between adjacent frequency slices explicitly. During low-rank matrix factorization, these similarities translate to alignment of subspaces of the factors, a notion we propose to employ as we reconstruct monochromatic frequency slices recursively starting at the low frequencies. While this idea is relatively simple in its core, to turn this recent insight into a successful scalable wavefield reconstruction scheme for 3D seismic requires a number of important steps. First, we need to move the weighting matrices, which encapsulate the prior information from adjacent frequency slices, from the objective to the data misfit constraint. This move considerably improves the performance of the weighted low-rank matrix factorization on which our wavefield reconstructions is based. Secondly, we introduce approximations that allow us to decouple computations on a row-by-row and column-by-column basis, which in turn allow to parallelize the alternating optimization on which our low-rank factorization relies. The combination of weighting and decoupling leads to a computationally feasible full-azimuth wavefield reconstruction scheme that scales to industry-scale problem sizes. We demonstrate the performance of the proposed parallel algorithm on a 2D field data and on a 3D synthetic dataset. In both cases our approach produces high-fidelity broadband wavefield reconstructions from severely subsampled data.},
	keywords = {5D reconstruction, compressed sensing, frequency-domain, parallel, signal processing},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2020/sharan2020lsh/sharan2020lsh.html},
	author = {Shashin Sharan and Yijun Zhang and Oscar Lopez and Felix J. Herrmann}
}
@conference {rizzuti2020SEGuqavp,
	title = {Parameterizing uncertainty by deep invertible networks, an application to reservoir characterization},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2020},
	note = {(SEG, virtual)},
	month = {09},
	pages = {1541-1545},
	abstract = {Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This analysis allows to assess the confidence in the candidate solution and how it is reflected in the tasks that are typically performed after imaging (e.g., stratigraphic segmentation following reservoir characterization). Classically, uncertainty comes in the form of a probability distribution formulated from Bayesian principles, from which we seek to obtain samples. A popular solution involves Monte Carlo sampling. Here, we propose instead an approach characterized by training a deep network that "pushes forward" Gaussian random inputs into the model space (representing, for example, density or velocity) as if they were sampled from the actual posterior distribution. Such network is designed to solve a variational optimization problem based on the Kullback-Leibler divergence between the posterior and the network output distributions. This work is fundamentally rooted in recent developments for invertible networks. Special invertible architectures, besides being computational advantageous with respect to traditional networks, do also enable analytic computation of the output density function. Therefore, after training, these networks can be readily used as a new prior for a related inversion problem. This stands in stark contrast with Monte-Carlo methods, which only produce samples. We validate these ideas with an application to angle-versus-ray parameter analysis for reservoir characterization.},
	keywords = {Full-waveform inversion, SEG, Uncertainty quantification},
	doi = {10.1190/segam2020-3428150.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/rizzuti2020SEGuqavp/rizzuti2020SEGuqavp.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/rizzuti2020SEGuqavp/rizzuti2020SEGuqavp_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/rizzuti2020SEGuqavp/rizzuti2020SEGuqavp_pres.mp4},
	software = {https://github.com/slimgroup/Software.SEG2020},
	author = {Gabrio Rizzuti and Ali Siahkoohi and Philipp A. Witte and Felix J. Herrmann}
}
@conference {siahkoohi2020SIAMISsiu,
	title = {Seismic Imaging with Uncertainty Quantification: Sampling from the Posterior with Generative Networks},
	booktitle = {SIAM Conference on Imaging Science},
	year = {2020},
	note = {IS20},
	month = {7},
	abstract = {n/a},
	keywords = {Imaging, invertible networks, IS20, McMC, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMIS/2020/siahkoohi2020SIAMISsiu/siahkoohi2020SIAMISsiu_pres.pdf},
	author = {Ali Siahkoohi and Philipp A. Witte and Mathias Louboutin and Felix J. Herrmann and Gabrio Rizzuti}
}
@conference {zhang2020SEGtli,
	title = {Transfer learning in large-scale ocean bottom seismic wavefield reconstruction},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2020},
	note = {(SEG, virtual)},
	month = {09},
	pages = {1666-1670},
	abstract = {Achieving desirable receiver sampling in ocean bottom acquisition is often not possible because of cost considerations. Assuming adequate source sampling is available, which is achievable by virtue of reciprocity and the use of modern randomized (simultaneous-source) marine acquisition technology, we are in a position to train convolutional neural networks (CNNs) to bring the receiver sampling to the same spatial grid as the dense source sampling. To accomplish this task, we form training pairs consisting of densely sampled data and artificially subsampled data using a reciprocity argument and the assumption that the source-site sampling is dense. While this approach has successfully been used on the recovery monochromatic frequency slices, its application in practice calls for wavefield reconstruction of time-domain data. Despite having the option to parallelize, the overall costs of this approach can become prohibitive if we decide to carry out the training and recovery independently for each frequency. Because different frequency slices share information, we propose the use the method of transfer training to make our approach computationally more efficient by warm starting the training with CNN weights obtained from a neighboring frequency slices. If the two neighboring frequency slices share information, we would expect the training to improve and converge faster. Our aim is to prove this principle by carrying a series of carefully selected experiments on a relatively large-scale five-dimensional data synthetic data volume associated with wide-azimuth 3D ocean bottom node acquisition. From these experiments, we observe that by transfer training we are able t significantly speedup in the training, specially at relatively higher frequencies where consecutive frequency slices are more correlated.},
	keywords = {SEG, transfer learning, wavefield reconstruction},
	doi = {10.1190/segam2020-3427882.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/zhang2020SEGtli/zhang2020SEGtli.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/zhang2020SEGtli/zhang2020SEGtli_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/zhang2020SEGtli/zhang2020SEGtli_pres.mp4},
	software = {https://github.com/slimgroup/Software.SEG2020},
	author = {Mi Zhang and Ali Siahkoohi and Felix J. Herrmann}
}
@conference {siahkoohi2020SEGuqi,
	title = {Uncertainty quantification in imaging and automatic horizon tracking{\textemdash}a Bayesian deep-prior based approach},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2020},
	note = {(SEG, virtual)},
	month = {09},
	pages = {1636-1640},
	abstract = {In inverse problems, uncertainty quantification (UQ) deals with a probabilistic description of the solution nonuniqueness and data noise sensitivity. Setting seismic imaging into a Bayesian framework allows for a principled way of studying uncertainty by solving for the model posterior distribution. Imaging, however, typically constitutes only the first stage of a sequential workflow, and UQ becomes even more relevant when applied to subsequent tasks that are highly sensitive to the inversion outcome. In this paper, we focus on how UQ trickles down to horizon tracking for the determination of stratigraphic models and investigate its sensitivity with respect to the imaging result. As such, the main contribution of this work consists in a data-guided approach to horizon tracking uncertainty analysis. This work is fundamentally based on a special reparameterization of reflectivity, known as "deep prior". Feasible models are restricted to the output of a convolutional neural network with a fixed input, while weights and biases are Gaussian random variables. Given a deep prior model, the network parameters are sampled from the posterior distribution via a Markov chain Monte Carlo method, from which the conditional mean and point-wise standard deviation of the inferred reflectivities are approximated. For each sample of the posterior distribution, a reflectivity is generated, and the horizons are tracked automatically. In this way, uncertainty on model parameters naturally translates to horizon tracking. As part of the validation for the proposed approach, we verified that the estimated confidence intervals for the horizon tracking coincide with geologically complex regions, such as faults.},
	keywords = {horizon picking, Imaging, machine learning, SEG, Uncertainty quantification},
	doi = {10.1190/segam2020-3417560.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGuqi/siahkoohi2020SEGuqi.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGuqi/siahkoohi2020SEGuqi_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGuqi/siahkoohi2020SEGuqi_pres.mp4},
	software = {https://github.com/slimgroup/Software.SEG2020},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {siahkoohi2020SIAMTXLAudg,
	title = {Unsupervised data-guided uncertainty analysis in imaging and horizon tracking},
	booktitle = {SIAM Texas-Louisiana},
	year = {2020},
	note = {SIAMTXLA},
	month = {10},
	abstract = {Imaging typically is the first stage of a sequential workflow, and uncertainty quantification becomes more relevant when applied to subsequent tasks. We propose a Bayesian approach to horizon tracking uncertainty analysis, where we deploy a deep prior instead of adhering to handcrafted priors. By passing samples from the posterior distribution obtained via stochastic gradient Langevin dynamics to an automatic horizon tracker, we are able to incorporate the uncertainty on model parameters into horizon tracking.},
	keywords = {deep learning, horizon tracking, McMC, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMTXLA/2020/siahkoohi2020SIAMTXLAudg/siahkoohi2020SIAMTXLAudg_pres.pdf},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Mathias Louboutin and Felix J. Herrmann}
}
@conference {zhang2020SEGwrw,
	title = {Wavefield recovery with limited-subspace weighted matrix factorizations},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2020},
	note = {(SEG, virtual)},
	month = {09},
	pages = {2858-2862},
	abstract = {Modern-day seismic imaging and monitoring technology increasingly rely on dense full-azimuth sampling. Unfortunately, the costs of acquiring densely sampled data rapidly become prohibitive and we need to look for ways to sparsely collect data, e.g. from sparsely distributed ocean bottom nodes, from which we then derive densely sampled surveys through the method of wavefield reconstruction. Because of their relatively cheap and simple calculations, wavefield reconstruction via matrix factorizations has proven to be a viable and scalable alternative to the more generally used transform-based methods. While this method is capable of processing all full azimuth data frequency by frequency slice, its performance degrades at higher frequencies because monochromatic data at these frequencies is not as well approximated by low-rank factorizations. We address this problem by proposing a recursive recovery technique, which involves weighted matrix factorizations where recovered wavefields at the lower frequencies serve as prior information for the recovery of the higher frequencies. To limit the adverse effects of potential overfitting, we propose a limited-subspace recursively weighted matrix factorization approach where the size of the row and column subspaces to construct the weight matrices is constrained. We apply our method to data collected from the Gulf of Suez, and our results show that our limited-subspace weighted recovery method significantly improves the recovery quality.},
	keywords = {algorithm, data reconstruction, frequency-domain, interpolation, Processing, SEG},
	doi = {10.1190/segam2020-3428365.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/zhang2020SEGwrw/zhang2020SEGwrw.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/zhang2020SEGwrw/zhang2020SEGwrw_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/zhang2020SEGwrw/zhang2020SEGwrw_pres.mp4},
	software = {https://github.com/slimgroup/Software.SEG2020},
	author = {Yijun Zhang and Shashin Sharan and Oscar Lopez and Felix J. Herrmann}
}
@conference {siahkoohi2020SEGwdp,
	title = {Weak deep priors for seismic imaging},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2020},
	note = {(SEG, virtual)},
	month = {09},
	pages = {2998-3002},
	abstract = {Incorporating prior knowledge on model unknowns of interest is essential when dealing with ill-posed inverse problems due to the nonuniqueness of the solution and data noise. Unfortunately, it is not trivial to fully describe our priors in a convenient and analytical way. Parameterizing the unknowns with a convolutional neural network (CNN), and assuming an uninformative Gaussian prior on its weights, leads to a variational prior on the output space that favors "natural" images and excludes noisy artifacts, as long as overfitting is prevented. This is the so-called deep-prior approach. In seismic imaging, however, evaluating the forward operator is computationally expensive, and training a randomly initialized CNN becomes infeasible. We propose, instead, a weak version of deep priors, which consists of relaxing the requirement that reflectivity models must lie in the network range, and letting the unknowns deviate from the network output according to a Gaussian distribution. Finally, we jointly solve for the reflectivity model and CNN weights. The chief advantage of this approach is that the updates for the CNN weights do not involve the modeling operator, and become relatively cheap. Our synthetic numerical experiments demonstrate that the weak deep prior is more robust with respect to noise than conventional least-squares imaging approaches, with roughly twice the computational cost of reverse-time migration, which is the affordable computational budget in large-scale imaging problems.},
	keywords = {deep prior, machine learning, SEG, seismic imaging},
	doi = {10.1190/segam2020-3417568.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGwdp/siahkoohi2020SEGwdp.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGwdp/siahkoohi2020SEGwdp_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2020/siahkoohi2020SEGwdp/siahkoohi2020SEGwdp_pres.mp4},
	software = {https://github.com/slimgroup/Software.SEG2020},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@conference {herrmann2019EAGEHPCaii,
	title = {Accelerating ideation and innovation cheaply in the Cloud the power of abstraction, collaboration and reproducibility},
	booktitle = {4th EAGE Workshop on High-performance Computing},
	year = {2019},
	note = {(EAGE HPC Workshop, Dubai)},
	month = {10},
	keywords = {cloud, devito, EAGE, HPC, JUDI},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGEHPC/2019/herrmann2019EAGEHPCaii/herrmann2019EAGEHPCaii_pres.pdf},
	author = {Felix J. Herrmann and Charles Jones and Gerard Gorman and Jan H{\"u}ckelheim and Keegan Lensink and Paul H. J. Kelly and Navjot Kukreja and Henryk Modzelewski and Michael Lange and Mathias Louboutin and Fabio Luporini and James Selvages and Philipp A. Witte}
}
@conference {siahkoohi2019SEGdlb,
	title = {Deep-learning based ocean bottom seismic wavefield recovery},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2019},
	note = {(SEG, San Antonio)},
	month = {09},
	pages = {2232-2237},
	abstract = {Ocean bottom surveys usually suffer from having very sparse receivers. Assuming a desirable source sampling, achievable by existing methods such as (simultaneous-source) randomized marine acquisition, we propose a deep-learning based scheme to bring the receivers to the same spatial grid as sources using a convolutional neural network. By exploiting source-receiver reciprocity, we construct training pairs by artificially subsampling the fully-sampled single-receiver frequency slices using a random training mask and later, we deploy the trained neural network to fill-in the gaps in single-source frequency slices. Our experiments show that a random training mask is essential for successful wavefield recovery, even when receivers are on a periodic gird. No external training data is required and experiments on a 3D synthetic data set demonstrate that we are able to recover receivers for up to 90 \% missing receivers, missing either randomly or periodically, with a better recovery for random case, at low to midrange frequencies.},
	keywords = {machine learning, obn, reciprocity, reconstruction, SEG},
	doi = {10.1190/segam2019-3216632.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/siahkoohi2019SEGdlb/siahkoohi2019SEGdlb.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/siahkoohi2019SEGdlb/siahkoohi2019SEGdlb_pres.pdf},
	author = {Ali Siahkoohi and Rajiv Kumar and Felix J. Herrmann}
}
@conference {witte2019SEGedw,
	title = {Event-driven workflows for large-scale seismic imaging in the cloud},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2019},
	note = {(SEG, San Antonio)},
	month = {09},
	pages = {3984-3988},
	abstract = {Cloud computing has seen a large rise in popularity in recent years and is becoming a cost effective alternative to on-premise computing, with theoretically unlimited scalability. However, so far little progress has been made in adapting the cloud for high performance computing (HPC) tasks, such as seismic imaging and inversion. As the cloud does not provide the same type of fast and reliable connections as conventional HPC clusters, porting legacy codes developed for HPC environments to the cloud is ineffective and misses out on an opportunity to take advantage of new technologies presented by the cloud. We present a novel approach of bringing seismic imaging and inversion workflows to the cloud, which does not rely on a traditional HPC environment, but is based on serverless and event-driven computations. Computational resources are assigned dynamically in response to events, thus minimizing idle time and providing resilience to hardware failures. We test our workflow on two large-scale imaging examples and demonstrate that cost-effective HPC in the cloud is possible, but requires careful reconsiderations of how to bring software to the cloud.},
	keywords = {cloud, Imaging, large-scale, LS-RTM, RTM, SEG, workflow},
	doi = {10.1190/segam2019-3215069.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/witte2019SEGedw/witte2019SEGedw.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/witte2019SEGedw/witte2019SEGedw_pres.pdf},
	author = {Philipp A. Witte and Mathias Louboutin and Henryk Modzelewski and Charles Jones and James Selvage and Felix J. Herrmann}
}
@article {sharan2018fsp,
	title = {Fast sparsity-promoting microseismic source estimation},
	journal = {Geophysical Journal International},
	volume = {216},
	number = {1},
	year = {2019},
	note = {(Geophysical Journal International)},
	month = {01},
	pages = {164-181},
	abstract = {Microseismic events are generated during hydraulic fracturing of unconventional reservoirs and carry information on fracture locations and the origin times associated with these microseismic events. For drilling purposes and to prevent hazardous situations, we need to have accurate knowledge on the fracture locations as well as on their size, and their density. Because microseismic waves can travel far distances, microseismic data collected at the surface and or in boreholes can help us to monitor hydraulic fracturing. While so-called back propagation or time-reversal methods are able to focus recorded energy back onto the sources when a reasonable velocity model is available, these methods suffer from blurring especially in situations where the data acquisition suffers from lack of aperture, sparse sampling, and noise. As a result, these methods typically cannot resolve sources in close proximity, a desired feature since we need this information if we want to follow the fracture evolution in space and time. In that situation, we need to estimate the locations and the associated source-time functions for closely spaced microseismic sources along the active fractures. To overcome the limitations of time-reversal methods, we propose a wave-equation based inversion approach where we invert for the complete source wavefield in both space and time. By promoting sparsity on the source wavefield in space, we negate the effects of non-radiating sources during the inversion and obtain high-resolution intensity plots and high-fidelity estimates for the source-time functions. We obtain these results relatively fast by accelerating the linearized Bregman method with a dual formulation. Through experiments, we demonstrate that our method is computationally feasible, robust to noise, and works for closely spaced sources with overlapping source-time functions in complex geological settings.},
	keywords = {induced seismicity, Joint inversion, waveform inversion},
	doi = {10.1093/gji/ggy415},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalJournalInternational/2018/sharan2018fsp/sharan2018fsp.pdf},
	author = {Shashin Sharan and Rongrong Wang and Felix J. Herrmann}
}
@conference {zhang2019SEGhfw,
	title = {High-frequency wavefield recovery with weighted matrix factorizations},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2019},
	note = {(SEG, San Antonio)},
	month = {09},
	pages = {3959-3963},
	abstract = {Acquired seismic data is normally not the fully sampled data we would like to work with since traces are missing due to physical constraints or budget limitations. Rank minimization is an effective way to recovering the missing trace data. Unfortunately, this technique{\textquoteright}s performance may deteriorate at higher frequency because high-frequency data can not necessarily be captured accurately by low-rank matrix factorizations albeit remedies exist such as hierarchical semi-separable matrices. As a result, recovered data often suffers from low signal to noise ratio S/Rs at the higher frequencies. To deal with this situation, we propose a weighted recovery method that improves the performance at the high frequencies by recursively using information from matrix factorizations at neighboring lower frequencies. Essentially, we include prior information from previously reconstructed frequency slices during the wavefield reconstruction. We apply our method to data collected from the Gulf of Suez, which shows that our method performs well compared to the traditional method without weighting.},
	keywords = {algorithm, data reconstruction, frequency-domain, interpolation, Processing, SEG},
	doi = {10.1190/segam2019-3215103.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/zhang2019SEGhfw/zhang2019SEGhfw.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/zhang2019SEGhfw/zhang2019SEGhfw_pres.pdf},
	author = {Yijun Zhang and Shashin Sharan and Felix J. Herrmann}
}
@article {siahkoohi2019itl,
	title = {The importance of transfer learning in seismic modeling and imaging},
	journal = {Geophysics},
	year = {2019},
	note = {(GEOPHYSICS)},
	abstract = {Accurate forward modeling is essential for solving inverse problems in exploration seismology. Unfortunately, it is often not possible to afford being physically or numerically accurate. To overcome this conundrum, we make use of raw and processed data from nearby surveys. We propose to use this data, consisting of shot records or velocity models, to pre-train a neural network to correct for the effects of, for instance, the free surface or numerical dispersion, both of which can be considered as proxies for incomplete or inaccurate physics. Given this pre-trained neural network, we apply transfer learning to finetune this pre-trained neural network so it performs well on its task of mapping low-cost, but low-fidelity, solutions to high-fidelity solutions for the current survey. As long as we can limit ourselves during finetuning to using only a small fraction of high-fidelity data, we gain processing the current survey while using information from nearby surveys. We demonstrate this principle by removing surface-related multiples and ghosts from shot records and the effects of numerical dispersion from migrated images and wave simulations},
	keywords = {deep learning, Imaging, Modeling, SRME, transfer learning},
	doi = {10.1190/geo2019-0056.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2019/siahkoohi2019itl/siahkoohi2019itl.html},
	author = {Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@conference {herrmann2019NIPSliwcuc,
	title = {Learned imaging with constraints and uncertainty quantification},
	booktitle = {Neural Information Processing Systems (NeurIPS)},
	year = {2019},
	note = {(NIPS, Vancouver)},
	month = {12},
	abstract = {We outline new approaches to incorporate ideas from convolutional networks into wave-based least-squares imaging. The aim is to combine hand-crafted constraints with deep convolutional networks allowing us to directly train a network capable of generating samples from the posterior. The main contributions include combination of weak deep priors with hard handcrafted constraints and a possible new way to sample the posterior.},
	keywords = {constraint, deep learning, Imaging, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2019/herrmann2019NIPSliwcuc/herrmann2019NIPSliwcuc.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2019/herrmann2019NIPSliwcuc/herrmann2019NIPSliwcuc_pres.pdf},
	url2 = {https://openreview.net/pdf?id=Hyet2Q29IS},
	author = {Felix J. Herrmann and Ali Siahkoohi and Gabrio Rizzuti}
}
@presentation {herrmann2019HOTCSEliwcuq,
	title = {Learned imaging with constraints and uncertainty quantification},
	year = {2019},
	note = {(HotCSE)},
	abstract = {We outline new approaches to incorporate ideas from convolutional networks into wave-based least-squares imaging. The aim is to combine hand-crafted constraints with deep convolutional networks allowing us to directly train a network capable of generating samples from the posterior. The main contributions include combination of weak deep priors with hard handcrafted constraints and a possible new way to sample the posterior.},
	keywords = {deep learning, Expectation Maximization, HotCSE, Imaging, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Lectures/HotCSE/2019/herrmann2019HOTCSEliwcuq/herrmann2019HOTCSEliwcuq.pdf},
	author = {Felix J. Herrmann and Ali Siahkoohi and Gabrio Rizzuti}
}
@conference {rizzuti2019EAGElis,
	title = {Learned iterative solvers for the Helmholtz equation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2019},
	note = {(EAGE, Copenhagen)},
	month = {06},
	abstract = {We propose a {\textquoteleft}learned{\textquoteright} iterative solver for the Helmholtz equation, by combining traditional Krylov-based solvers with machine learning. The method is, in principle, able to circumvent the shortcomings of classical iterative solvers, and has clear advantages over purely data-driven ap- proaches. We demonstrate the effectiveness of this approach under a 1.5-D assumption, when ade- quate a priori information about the velocity distribution is known.},
	keywords = {EAGE, Helmholtz, Iterative, machine learning},
	doi = {10.3997/2214-4609.201901542},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2019/rizzuti2019EAGElis/rizzuti2019EAGElis.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2019/rizzuti2019EAGElis/rizzuti2019EAGElis_pres.pdf},
	author = {Gabrio Rizzuti and Ali Siahkoohi and Felix J. Herrmann}
}
@techreport {siahkoohi2019TRnna,
	title = {Neural network augmented wave-equation simulation},
	number = {TR-CSE-2019-1},
	year = {2019},
	month = {09},
	institution = {Georgia Institute of Technology},
	abstract = {Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with incomplete physics. One proxy of incomplete physics is an inaccurate discretization of Laplacian in simulation of wave equation via finite-difference method. We exploit intrinsic one-to-one similarities between timestepping algorithm with Convolutional Neural Networks (CNNs), and propose to intersperse CNNs between low-fidelity timesteps. Augmenting neural networks with low-fidelity timestepping algorithms may allow us to take large timesteps while limiting the numerical dispersion artifacts. While simulating the wave-equation with low-fidelity timestepping algorithm, by correcting the wavefield several time during propagation, we hope to limit the numerical dispersion artifact introduced by a poor discretization of the Laplacian. As a proof of concept, we demonstrate this principle by correcting for numerical dispersion by keeping the velocity model fixed, and varying the source locations to generate training and testing pairs for our supervised learning algorithm.},
	keywords = {deep learning, finite difference, wave equation},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2019/siahkoohi2019TRnna/siahkoohi2019TRnna.html},
	url2 = {https://arxiv.org/pdf/1910.00925.pdf},
	author = {Ali Siahkoohi and Mathias Louboutin and Felix J. Herrmann}
}
@conference {siahkoohi2019SEGsrm,
	title = {Surface-related multiple elimination with deep learning},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2019},
	note = {(SEG, San Antonio)},
	month = {09},
	pages = {4629-4634},
	abstract = {We explore the potential of neural networks in approximating the action of the computationally expensive Estimation of Primaries by Sparse Inversion (EPSI) algorithm, applied to real data, via a supervised learning algorithm. We show that given suitable training data, consisting of a relatively cheap prediction of multiples and pairs of shot records with and without surface-related multiples, obtained via EPSI, a well-trained neural network is capable of providing an approximation to the action of the EPSI algorithm. We perform our numerical experiment on the field Nelson data set. Our results demonstrate that the quality of the multiple elimination via our neural network improves compared to the case where we only feed the network with shot records with surface-related multiples. We take these benefits by supplying the neural network with a relatively poor prediction of the multiples, e.g. obtained by a relatively cheap single step of Surface-Related Multiple Elimination.},
	keywords = {EPSI, machine learning, SEG, SRME},
	doi = {10.1190/segam2019-3216723.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/siahkoohi2019SEGsrm/siahkoohi2019SEGsrm.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2019/siahkoohi2019SEGsrm/siahkoohi2019SEGsrm_pres.pdf},
	author = {Ali Siahkoohi and Dirk J. Verschuur and Felix J. Herrmann}
}
@conference {kumar2018EAGEcsb,
	title = {Compressed sensing based land simultaneous acquisition using encoded sweeps},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2018},
	note = {(EAGE, Copenhagen)},
	month = {06},
	abstract = {Simultaneous shooting methods using encoded sweeps can enhance the productivity of land acquisition in situations where deployment of many vibrators and larger receiver spread is not possible in the field due to obstructions or permit limitations. However, the existing framework requires shooting the full sequence of encoded sweeps on each shot point to reconstruct the complete frequency bandwidth Green{\textquoteright}s function. Although this simultaneous shooting method reduces the sweeping time vs conventional sequential shooting, the gain in efficiency is limited. To further reduce the sweeping time, we propose to acquire randomly selected subsets of the encoded sweeps sequences followed by a rank-minimization based joint source separation and spectral interpolation framework to reconstruct the full bandwidth deblended Green{\textquoteright}s function. We demonstrate the advantages of proposed sampling and reconstruction framework using a synthetic seismic line simulated using SEG-SEAM Phase II land velocity and density model.},
	keywords = {compressed sensing, EAGE, land, SEAM, source separation, spectral interpolation},
	doi = {10.3997/2214-4609.201800643},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2018/kumar2018EAGEcsb/kumar2018EAGEcsb.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2018/kumar2018EAGEcsb/kumar2018EAGEcsb_pres.pdf},
	author = {Rajiv Kumar and Shashin Sharan and Nick Moldoveanu and Felix J. Herrmann}
}
@conference {sharan2018SEGada,
	title = {A debiasing approach to microseismic},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2018},
	note = {(SEG, Anaheim)},
	month = {10},
	pages = {2942-2946},
	abstract = {Microseismic data is often used to locate fracture locations and their origin in time created by fracking. Although surface microseismic data can have large apertures and is easier to acquire than the borehole data, it often suffers from poor signal to noise ratio (S/R). Poor S/R poses a challenge in terms of estimating the correct location and source-time function of a microseismic source. In this work, we propose a denoising step in combination with a computationally cheap debiasing based approach to locate microseismic sources and to estimate their source-time functions with correct amplitude from extremely noisy data. Through numerical experiments, we demonstrate that our method can work with closely spaced microseismic sources with source-time functions of different peak amplitudes and frequencies. We have also shown the ability of our method with the smooth velocity model.},
	keywords = {Full-waveform inversion, Imaging, microseismic, noise, SEG, wave equation},
	doi = {10.1190/segam2018-2997252.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/sharan2018SEGada/sharan2018SEGada.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/sharan2018SEGada/sharan2018SEGada_pres.pdf},
	author = {Shashin Sharan and Rajiv Kumar and Rongrong Wang and Felix J. Herrmann}
}
@conference {siahkoohi2018SEGcnn,
	title = {Deep Convolutional Neural Networks in prestack seismic{\textendash}-two exploratory examples},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2018},
	note = {(SEG, Anaheim)},
	month = {10},
	pages = {2196-2200},
	abstract = {Deep convolutional neural networks are having quite an impact and have resulted in step changes in the capabilities of image and voice recognition systems and there are indications they may have a similar impact on post-stack seismic images. While these developments are certainly important, we are after all dealing with an imaging problem involving an unknown earth and not completely understood physics. When the imaging step itself is not handled properly, this may possibly offset gains offered by deep learning. Motivated by our work on deep convolutional neural networks in seismic data reconstruction, we discuss how generative networks can be employed in prestack problems ranging from the relatively mondane removal of the effects of the free surface to dealing with the complex effects of numerical dispersion in time-domain finite differences. While the results we present are preliminary, there are strong indications that generative deep convolutional neural networks can have a major impact on complex tasks in prestack seismic data processing and modeling for inversion.},
	keywords = {Dispersion, machine learning, Modeling, Processing, SEG, SRME},
	doi = {10.1190/segam2018-2998599.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/siahkoohi2018SEGcnn/siahkoohi2018SEGcnn.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2018/siahkoohi2018SEGcnn/siahkoohi2018SEGcnn_pres.pdf},
	author = {Ali Siahkoohi and Mathias Louboutin and Rajiv Kumar and Felix J. Herrmann}
}
@conference {herrmann2018SMCtpa,
	title = {The power of abstraction in Computational Exploration Seismology},
	booktitle = {Smoky Mountains Computational Sciences and Engineering Conference},
	year = {2018},
	month = {08},
	abstract = {The field of Computational Exploration Seismology has over the years benefited tremendously from developments in HPC. Back in the 80{\textquoteright}s and early 90{\textquoteright}s, the oil \& gas industry was among the main drivers of HPC technology with a resurgence about ten years ago with the advent of full-waveform inversion-i.e., an adjoint-state method for inverse problems that involve the wave equation. While the combination of hardware developments and tedious manual coding efforts have resulted in major improvements, the rate of innovations is slow in part because of the inherent complexities of the mostly monolithic code bases. As a result, innovations make it too slowly into these optimized codes. This stifles innovation and could prevent adaptation of important developments such as machine learning with deep convolutional neural networks into existing workflows. In comparison, the technological advances in the academic as well as commercial machine learning communities have been much faster in part because of robust and well abstracted code bases such as PyTorch and TensorFlow. Since both machine learning and adjoint-state methods rely on back propagation strong similarities exist ready to be exploited. During my talk, I will discuss lessons we learned in finding the appropriate abstractions, read Domain Specific Language, for time-stepping stencil-based finite differences in Devito, and how this is relevant for machine learning with deep networks. I will also share a vision on how ideas from machine learning can be merged into the development of the next-generation of wave-equation based imaging codes. In particular, I will demonstrate the remarkable ability of deep convolutional networks to map low-fidelity dispersed numerical wave simulations to high-fidelity ones. I feel that this apparently generalizable capability of neural nets opens a complete new approach to tackle fundamental problems in computational exploration seismology.},
	keywords = {SMC},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SMC/2018/herrmann2018SMCtpa/herrmann2018SMCtpa_pres.pdf},
	author = {Felix J. Herrmann and Gerard J. Gorman and Jan H{\"u}ckelheim and Keegan Lensink and Paul H. J. Kelly and Navjot Kukreja and Henryk Modzelewski and Michael Lange and Mathias Louboutin and Fabio Luporini and Ali Siahkoohi and Philipp A. Witte}
}
@article {peters2018pmf,
	title = {Projection methods and applications for seismic nonlinear inverse problems with multiple constraints},
	journal = {Geophysics},
	volume = {84},
	number = {2},
	year = {2018},
	note = {(Geophysics)},
	month = {02},
	pages = {R251-R269},
	abstract = {Nonlinear inverse problems are often hampered by non-uniqueness and local minima because of missing low frequencies and far offsets in the data, lack of access to good starting models, noise, and modeling errors. A well-known approach to counter these deficiencies is to include prior information on the unknown model, which regularizes the inverse problem. While conventional regularization methods have resulted in enormous progress in ill-posed (geophysical) inverse problems, challenges remain when the prior information consists of multiple pieces. To handle this situation, we propose an optimization framework that allows us to add multiple pieces of prior information in the form of constraints. Compared to additive regularization penalties, constraints have a number of advantages making them more suitable for inverse problems such as full-waveform inversion. The proposed framework is rigorous because it offers assurances that multiple constraints are imposed uniquely at each iteration, irrespective of the order in which they are invoked. To project onto the intersection of multiple sets uniquely, we employ Dykstra{\textquoteright}s algorithm that scales to large problems and does not rely on trade-off parameters. In that sense, our approach differs substantially from approaches such as Tikhonov regularization, penalty methods, and gradient filtering. None of these offer assurances, which makes them less suitable to full-waveform inversion where unrealistic intermediate results effectively derail the iterative inversion process. By working with intersections of sets, we keep expensive objective and gradient calculations unaltered, separate from projections, and we also avoid trade-off parameters. These features allow for easy integration into existing code bases. In addition to more predictable behavior, working with constraints also allows for heuristics where we built up the complexity of the model gradually by relaxing the constraints. This strategy helps to avoid convergence to local minima that represent unrealistic models. We illustrate this unique feature with examples of varying complexity.},
	keywords = {constraints, Full-waveform inversion, intersection, Optimization, projection, regularization},
	doi = {10.1190/geo2018-0192.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2018/peters2018pmf/peters2018pmf.html},
	author = {Bas Peters and Brendan R. Smithyman and Felix J. Herrmann}
}
@conference {siahkoohi2018EAGEsdr,
	title = {Seismic data reconstruction with Generative Adversarial Networks},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2018},
	note = {(EAGE, Copenhagen)},
	month = {06},
	abstract = {A main challenge in seismic imaging is acquiring densely sampled data. Compressed Sensing has provided theoretical foundations upon which desired sampling rate can be achieved by applying a sparsity promoting algorithm on sub-sampled data. The key point in successful recovery is to deploy a randomized sampling scheme. In this paper, we propose a novel deep learning-based method for fast and accurate reconstruction of heavily under-sampled seismic data, regardless of type of sampling. A neural network learns to do reconstruction directly from data via an adversarial process. Once trained, the reconstruction can be done by just feeding the frequency slice with missing data into the neural network. This adaptive nonlinear model makes the algorithm extremely flexible, applicable to data with arbitrarily type of sampling. With the assumption that we have access to training data, the quality of reconstructed slice is superior even for extremely low sampling rate (as low as 10\%) due to the data-driven nature of the method.},
	keywords = {data reconstruction, EAGE, generative adversarial networks, machine learning},
	doi = {10.3997/2214-4609.201801393},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2018/siahkoohi2018EAGEsdr/siahkoohi2018EAGEsdr.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2018/siahkoohi2018EAGEsdr/siahkoohi2018EAGEsdr_pres.pdf},
	author = {Ali Siahkoohi and Rajiv Kumar and Felix J. Herrmann}
}
@conference {sharan2018IEEEIUSspoa,
	title = {Sparsity-promoting photoacoustic imaging with source estimation},
	booktitle = {2018 IEEE International Ultrasonics Symposium (IUS)},
	year = {2018},
	note = {(IEEE IUS, Kobe)},
	month = {10},
	pages = {206-212},
	abstract = {Photoacoustics has emerged as a high-contrast imaging modality that provides optical absorption maps inside of tissues, therefore complementing morphological information of conventional ultrasound. The laser-generated photoacoustic waves are usually envelope-detected, thus disregarding the specific waveforms generated by each photoabsorber. Here we propose a sparsity-promoting image reconstruction method that allows the estimation of each photoabsorber{\textquoteright}s source-time function. Preliminary studies showed the ability to reconstruct the optical absorption map of an in silico vessel phantom. By using a sparsity-promoting imaging method, absorption maps and source-time functions can still be recovered even in situations where the number of transducers is decreased by a factor of six. Moreover, the recovery is able to attain higher resolution than conventional beamforming methods. Because our method recovers the source-time function of the absorbers, it could potentially also be used to distinguish different types of photoabsorbers, or the degree of aggregation of exogenous agents, under the assumption that these would generate different source-time functions at the moment of laser irradiation.},
	keywords = {Acceleration, estimation, IEEE, Image reconstruction, Phantoms, photoacoustic imaging, source-time function, sparsity promoting inversion, Transducers, wave equation},
	doi = {10.1109/ULTSYM.2018.8580037},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/IEEEIUS/2018/sharan2018IEEEIUSspoa/sharan2018IEEEIUSspoa.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IEEEIUS/2018/sharan2018IEEEIUSspoa/sharan2018IEEEIUSspoa_pres.pdf},
	author = {Shashin Sharan and Rajiv Kumar and Diego S. Dumani and Mathias Louboutin and Rongrong Wang and Stanislav Emelianov and Felix J. Herrmann}
}
@conference {sharan2017SEGhrf,
	title = {High resolution fast microseismic source collocation and source time function estimation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {2778-2783},
	abstract = {Sparsity promotion based joint microseismic source collocation and source time function estimation, using Linearized Bregman algorithm, although simple to implement, suffers from slow convergence. This is due to the fact that Linearized Bregman algorithm has only first order of convergence. In this work, we propose to accelerate the existing Linearized Bregman algorithm using the L-BFGS algorithm. Without any initial guess for the source location or source time function, our method is able to estimate the source location and source time function for kinematically correct smooth velocity model. We demonstrate the effectiveness of our method for multiple sources spaced within half a wavelength. We also compare our results with Linearized Bregman based method in {\textquoteleft}{\textquoteleft}2.5{\textquoteleft}{\textquoteleft}D instead of {\textquoteleft}{\textquoteleft}2{\textquoteleft}{\textquoteleft}D.},
	keywords = {algorithm, Full-waveform inversion, microseismic, passive imaging, SEG, wave equation},
	doi = {10.1190/segam2017-17787749.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/sharan2017SEGhrf/sharan2017SEGhrf.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/sharan2017SEGhrf/sharan2017SEGhrf_pres.pdf},
	author = {Shashin Sharan and Rongrong Wang and Felix J. Herrmann}
}
@article {kumar2017hrc,
	title = {Highly repeatable 3D compressive full-azimuth towed-streamer time-lapse acquisition {\textendash}- a numerical feasibility study at scale},
	journal = {The Leading Edge},
	volume = {36},
	number = {8},
	year = {2017},
	note = {(The Leading Edge)},
	month = {08},
	pages = {677-687},
	abstract = {Most conventional 3D time-lapse (or 4D) acquisitions are ocean-bottom cable (OBC) or ocean-bottom node (OBN) surveys since these surveys are relatively easy to replicate compared to towed-streamer surveys. To attain high degrees of repeatability, survey replicability and dense periodic sampling has become the norm for 4D surveys that renders this technology expensive. Conventional towed-streamer acquisitions suffer from limited illumination of subsurface due to narrow azimuth. Although, acquisition techniques such as multi-azimuth, wide-azimuth, rich-azimuth acquisition, etc., have been developed to illuminate the subsurface from all possible angles, these techniques can be prohibitively expensive for densely sampled surveys. This leads to uneven sampling, i.e., dense receiver and coarse source sampling or vice-versa, in order to make these acquisitions more affordable. Motivated by the design principles of Compressive Sensing (CS), we acquire economic, randomly subsampled (or compressive) and simultaneous towed-streamer time-lapse data without the need of replicating the surveys. We recover densely sampled time-lapse data on one and the same periodic grid by using a joint-recovery model (JRM) that exploits shared information among different time-lapse recordings, coupled with a computationally cheap and scalable rank-minimization technique. The acquisition is low cost since we have subsampled measurements (about 70\% subsampled), simulated with a simultaneous long-offset acquisition configuration of two source vessels travelling across a survey area at random azimuths. We analyze the performance of our proposed compressive acquisition and subsequent recovery strategy by conducting a synthetic, at scale, seismic experiment on a 3D time-lapse model containing geological features such as channel systems, dipping and faulted beds, unconformities and a gas cloud. Our findings indicate that the insistence on replicability between surveys and the need for OBC/OBN 4D surveys can, perhaps, be relaxed. Moreover, this is a natural next step beyond the successful CS acquisition examples discussed in this special issue.},
	keywords = {3D, CS, marine, rank minimization, simultaneous long offset, time-lapse seismic},
	doi = {10.1190/tle36080677.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2017/kumar2017hrc/kumar2017hrc.html},
	author = {Rajiv Kumar and Haneet Wason and Shashin Sharan and Felix J. Herrmann}
}
@presentation {herrmann2017SINBADFhrc,
	title = {Highly repeatable 3D compressive full-azimuth towed-streamer time-lapse acquisition {\textendash}- a numerical feasibility study at scale},
	year = {2017},
	publisher = {SINBAD},
	abstract = {Most conventional 3D time-lapse (or 4D) acquisitions are ocean-bottom cable (OBC) or ocean-bottom node (OBN) surveys since these surveys are relatively easy to replicate compared to towed-streamer surveys. To attain high degrees of repeatability, survey replicability and dense periodic sampling has become the norm for 4D surveys that renders this technology expensive. Conventional towed-streamer acquisitions suffer from limited illumination of subsurface due to narrow azimuth. Although, acquisition techniques such as multi-azimuth, wide-azimuth, rich-azimuth acquisition, etc., have been developed to illuminate the subsurface from all possible angles, these techniques can be prohibitively expensive for densely sampled surveys. This leads to uneven sampling, i.e., dense receiver and coarse source sampling or vice-versa, in order to make these acquisitions more affordable. Motivated by the design principles of Compressive Sensing (CS), we acquire economic, randomly subsampled (or compressive) and simultaneous towed-streamer time-lapse data without the need of replicating the surveys. We recover densely sampled time-lapse data on one and the same periodic grid by using a joint-recovery model (JRM) that exploits shared information among different time-lapse recordings, coupled with a computationally cheap and scalable rank-minimization technique. The acquisition is low cost since we have subsampled measurements (about 70\% subsampled), simulated with a simultaneous long-offset acquisition configuration of two source vessels travelling across a survey area at random azimuths. We analyze the performance of our proposed compressive acquisition and subsequent recovery strategy by conducting a synthetic, at scale, seismic experiment on a 3D time-lapse model containing geological features such as channel systems, dipping and faulted beds, unconformities and a gas cloud. Our findings indicate that the insistence on replicability between surveys and the need for OBC/OBN 4D surveys can, perhaps, be relaxed. Moreover, this is a natural next step beyond the successful CS acquisition examples discussed during this session.},
	keywords = {Presentation, SINBAD, SINBADFALL2017, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/herrmann2017SINBADFhrc/herrmann2017SINBADFhrc.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/herrmann2017SINBADFhrc/herrmann2017SINBADFhrc.mov},
	author = {Felix J. Herrmann and Rajiv Kumar and Haneet Wason and Shashin Sharan and Felix Oghenekohwo}
}
@presentation {siahkoohi2017SINBADFsdi,
	title = {Seismic data interpolation with Generative Adversarial Networks},
	year = {2017},
	publisher = {SINBAD},
	abstract = {In this project we implement an algorithm to predict the missing traces in the seismic shot gathers. The missing traces can be either regular or irregular. Any interpolation scheme assumes a prior knowledge on the data. Here the prior information used to interpolate the data is obtained from interaction of two trained deep neural networks, namely Generator and Discriminator. The combination of these two neural networks is called Generative Adversarial Network (GAN). GAN is trained on finely sampled seismic shot gathers. By employing the trained GAN we can project shot gathers with missing traces into the domain of the generator network. Then by computing the output of generator given the found projection, we can fill in the initial gather.},
	keywords = {Presentation, SINBAD, SINBADFALL2017, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/siahkoohi2017SINBADFsdi/siahkoohi2017SINBADFsdi.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/siahkoohi2017SINBADFsdi/siahkoohi2017SINBADFsdi.mov},
	author = {Ali Siahkoohi and Felix J. Herrmann}
}
@presentation {sharan2017SINBADFtts,
	title = {Tracking the spatial-temporal evolution of fractures by microseismic source collocation},
	year = {2017},
	publisher = {SINBAD},
	abstract = {Unlike conventional reservoirs, unconventional plays are not naturally viable for economical production of oil and gas. They require stimulation by injecting high-pressure fluid causing fractures in the rocks. These fractures make the medium more permeable, hence, the extraction of oil and gas becomes feasible. For drilling purposes and to prevent potentially hazardous situations, we need to have good knowledge of the location of these fractures. Also, we need to have good knowledge about how these fractures originated in time. Hydraulic fracturing changes stress in rocks, which results in the emission of microseismic waves. The opening of cracks due to high pressure fluid injection during hydraulic fracturing mainly causes this change in stress in the rocks. Therefore, microseismic events are mostly localized along these fractures and have finite energy along time. To accurately track the evolution of fractures in both space and time, we need to locate closely spaced microseismic events along these fractures activating at very small time intervals. A naive approach can be the back propagation of the observed data to find out a point in space and time where maximum focusing of back propagating energy occurs. This point corresponds to the location and origin time of a microseismic source. This approach, although simpler, suffers from low resolution and requires scanning of complete 4D volume (3D in space and 1D in time). Hence, this method can be challenging when there are multiple closely spaced microseismic sources originating at different times. We in this work propose a sparsity promotion based method that can locate closely spaced microseismic events, with spatial separation as low as within half a wavelength, activating at small time intervals. We simultaneously estimate the origin time of microseismic events by estimating their source time functions. Our method exploits the fact that microseismic events are localized in space and have finite energy. We use accelerated Linearized Bregman algorithm with a preconditioning operator to arrive at a computationally feasible scheme.},
	keywords = {Presentation, SINBAD, SINBADFALL2017, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/sharan2017SINBADFtts/sharan2017SINBADFtts.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/sharan2017SINBADFtts/sharan2017SINBADFtts.mov},
	author = {Shashin Sharan and Rongrong Wang and Felix J. Herrmann}
}
@conference {herrmann2016SEGWSctl,
	title = {Compressive time-lapse marine acquisition},
	booktitle = {SEG Workshop on Low cost geophysics: How to be creative in a cost-challenged environment; Dallas},
	year = {2016},
	note = {(SEG Workshop, Dallas)},
	month = {10},
	keywords = {Acquisition, SEG, workshop},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/herrmann2016SEGWSctl/herrmann2016SEGWSctl_pres.pdf},
	author = {Felix J. Herrmann and Rajiv Kumar and Felix Oghenekohwo and Shashin Sharan and Haneet Wason}
}
@presentation {kumar2016SINBADFels,
	title = {Efficient large-scale 5D seismic data acquisition and processing using rank-minimization},
	year = {2016},
	publisher = {SINBAD},
	abstract = {Seismic data collection is becoming challenging because of increased demands for high-quality, long-offset and wide-azimuth data. Leveraging ideas from CS, in this work we establish a cost effective acquisition and processing techniques, which are no longer dominated by survey area size but by the sparsity of seismic data volumes. In the first part of abstract, we establish connections between random time dithering and jittered sampling in space. Specifically, we recover high-quality 5D seismic data volumes from time-jittered marine acquisition where the average inter-shot time is significantly reduced, leading to cheaper surveys due to fewer overlapping shots. The time-jittered acquisition, in conjunction with the shot separation by Singular-Value Decomposition (SVD)-free factorization based rank-minimization approach, allows us to recover high quality 5D seismic data volumes. Results are illustrated for simulations of simultaneous time-jittered continuous recording for a 3D ocean-bottom cable survey, where we outperforms existing techniques, by an order of magnitude computational speedup and using 1/20th of the memory, that use sparsity in transforms domains. The second part of abstract focussed on leveraging low-rank structure in seismic data to solve extremely large data recovery (interpolation) problems. We introduced a large{\textendash}scale SVD-free optimization framework that is robust with respect to outliers and that uses information on the support. We test the efficacy of the proposed interpolation framework on a large-scale 5D seismic data, generated from the geologically complex synthetic 3D Compass velocity model, where 80\% of the data has been removed. Our findings show that major computational and memory gains are possible compared to curvelet-based reconstruction.},
	keywords = {Presentation, SINBAD, SINBADFALL2016, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/kumar2016SINBADFels/kumar2016SINBADFels.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/kumar2016SINBADFels/kumar2016SINBADFels.mov},
	author = {Rajiv Kumar and Shashin Sharan and Haneet Wason and Felix J. Herrmann}
}
@presentation {sharan2016SINBADFhrm,
	title = {High resolution microseismic source collocation},
	year = {2016},
	publisher = {SINBAD},
	abstract = {Microseismic waves generated by hydraulic fracturing are used to locate the fractures created in the reservoir. Most of the existing source collocation methods have their limitations in terms of resolution of very closely spaced microseismic events. In this work we propose a method to collocate microseismic events with high resolution along with simultaneous estimation of source time function. In the context of waves, the finite-difference modelling operator acts as an analysis operator for wavefields. This implies that wavefields under the action of a finite-difference modelling kernel can be focused to sources generating these wavefields. We exploit this property of wavefields to locate microseismic events and estimate the source time function jointly. To arrive at a computational feasible scheme, we use the accelerated version of Linearized Bregman (LBR) algorithm to solve the above mentioned problem. This is joint work with Rongrong Wang.},
	keywords = {Presentation, SINBAD, SINBADFALL2016, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/sharan2016SINBADFhrm/sharan2016SINBADFhrm.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/sharan2016SINBADFhrm/sharan2016SINBADFhrm.mov},
	author = {Shashin Sharan and Rongrong Wang and Felix J. Herrmann}
}
@presentation {wason2016SINBADFlcr,
	title = {Low-cost, randomized 3D towed-marine time-lapse seismic acquisition},
	year = {2016},
	publisher = {SINBAD},
	abstract = {Most often conventional 3D towed-marine seismic data acquisition suffers from limited illumination of subsurface due to narrow azimuth. Although, acquisition techniques such as Ocean Bottom Cable (OBC), Ocean Bottom Node (OBN), Rich-Azimuth (RAZ) acquisition, Multi-Azimuth (MAZ) acquisition have been developed to illuminate the subsurface from all possible angles, these acquisition techniques are expensive. Motivated by the design principles of compressed sensing, we acquire randomly subsampled and simultaneous (e.g., simultaneous long offset) 3D towed-marine time-lapse seismic data for few (random) azimuths, and recover densely sampled multiple azimuth baseline and monitor data via sparsity promotion and rank minimization. Our acquisition is low cost since we have subsampled measurements.},
	keywords = {Presentation, SINBAD, SINBADFALL2016, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/wason2016SINBADFlcr/wason2016SINBADFlcr.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/wason2016SINBADFlcr/marine_acq_mask.pdf},
	author = {Rajiv Kumar and Felix Oghenekohwo and Shashin Sharan and Haneet Wason and Felix J. Herrmann}
}
@presentation {witte2016SINBADFpve,
	title = {Phase velocity error minimizing scheme for the anisotropic pure P-wave equation},
	year = {2016},
	publisher = {SINBAD},
	abstract = {Pure P-wave equations for acoustic modeling in transverse isotropic media are derived by approximating the exact pure P-wave dispersion relation. In this work, we present an alternative to the common Taylor expansion based equations, in which we approximate the exact dispersion relation through a polynomial expansion and determine its coefficients by solving a least squares problem that minimizes the phase velocity error over the complete range of phase angles. We show that this approach is up to an order of magnitude more accurate than other pure P-wave equations at a comparable computational cost.},
	keywords = {Presentation, SINBAD, SINBADFALL2016, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/witte2016SINBADFpve/witte2016SINBADFpve.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2016/Fall/witte2016SINBADFpve/witte2016SINBADFpve.mov},
	author = {Philipp A. Witte and Christiaan C. Stolk and Felix J. Herrmann}
}
@conference {witte2016SEGpve,
	title = {Phase velocity error minimizing scheme for the anisotropic pure P-wave equation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2016},
	note = {(SEG, Dallas)},
	month = {10},
	pages = {452-457},
	abstract = {Pure P-wave equations for acoustic modeling in transverse isotropic media are derived by approximating the exact pure Pwave dispersion relation. In this work, we present an alternative approach to the approximate dispersion relation of Etgen and Brandsberg-Dahl, in which we approximate the exact dispersion relation through a polynomial expansion and determine its coefficients by solving a linear least squares problem that minimizes the phase velocity error over the entire range of phase angles. The coefficients are also optimized over a pre-defined range of Thomsen parameters, so that the phase error is small for models with spatially varying anisotropy. Phase velocity error analysis shows that the optimized pure P-wave equation is up to one order of magnitude more accurate than other popular pure P-wave equations, even for highly non-elliptic anisotropy. The optimized equation can be easily turned into a time-domain forward modeling scheme and comparisons of the modeled waveforms with analytical travel times once more illustrate its high accuracy. We also provide an efficient implementation of our approach for 3D tilted TI media that limits the count of fast Fourier transforms per time step to a number that is comparable to other pure P-wave equations.},
	keywords = {anisotropy, least squares, Modelling, SEG, TTI},
	doi = {10.1190/segam2016-13844850.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/witte2016SEGpve/witte2016SEGpve.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/witte2016SEGpve/witte2016SEGpve_poster.pdf},
	author = {Philipp A. Witte and Christiaan C. Stolk and Felix J. Herrmann}
}
@conference {sharan2016SEGspj,
	title = {Sparsity-promoting joint microseismic source collocation and source-time function estimation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2016},
	note = {(SEG, Dallas)},
	month = {10},
	pages = {2574-2579},
	abstract = {In this work, we propose a new method to simultaneously locate microseismic events (e.g., induced by hydraulic fracturing) and estimate the source signature of these events. We use the method of linearized Bregman. This algorithm focuses unknown sources at their true locations by promoting sparsity along space and at the same time keeping the energy along time in check. We are particularly interested in situations where the microseismic data is noisy, sources have different signatures and we only have access to the smooth background-velocity model. We perform numerical experiments to demonstrate the usability of the proposed method. We also compare our results with full-waveform inversion based microseismic event collocation methods. Our method gives flexibility to simultaneously get a more accurate source image along with an estimate of the source-time function, which carries important information on the rupturing process and source mechanism.},
	keywords = {microseismic, noise, SEG, sources, sparse, wave equation},
	doi = {10.1190/segam2016-13871022.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/sharan2016SEGspj/sharan2016SEGspj.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/sharan2016SEGspj/sharan2016SEGspj_pres.pdf},
	author = {Shashin Sharan and Rongrong Wang and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {kumar2016SEGtjm,
	title = {Time-jittered marine acquisition{\textendash}-a rank-minimization approach for 5D source separation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2016},
	note = {(SEG, Dallas)},
	month = {10},
	pages = {119-123},
	abstract = {Simultaneous source marine acquisition has been recognized as an economic way of improving spatial sampling and speedup acquisition time, where a single- (or multiple-) source vessel fires at jittered source locations and time instances. Consequently, the acquired simultaneous data volume is processed to separate the overlapping shot records resulting in densely sampled data volume. It has been shown in the past that the simultaneous source acquisition design and source separation process can be setup as a compressed sensing problem, where conventional seismic data is reconstructed from simultaneous data via a sparsity-promoting optimization formulation. While the recovery quality of separated data is reasonably well, the recovery process can be computationally expensive due to transform-domain redundancy. In this paper, we present a computationally tractable rank-minimization algorithm to separate simultaneous data volumes. The proposed algorithm is suitable for large-scale seismic data, since it avoids singular-value decompositions and uses a low-rank based factorized formulation instead. Results are illustrated for simulations of simultaneous time-jittered continuous recording for a 3D ocean-bottom cable survey.},
	keywords = {5D, marine, SEG, source separation, time-jittered acquisition},
	doi = {10.1190/segam2016-13878249.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/kumar2016SEGtjm/kumar2016SEGtjm.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2016/kumar2016SEGtjm/kumar2016SEGtjm_pres.pdf},
	author = {Rajiv Kumar and Shashin Sharan and Haneet Wason and Felix J. Herrmann}
}
@conference {smithyman2015EAGEcwi,
	title = {Constrained waveform inversion of colocated VSP and surface seismic data},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {Constrained Full-Waveform Inversion (FWI) is applied to produce a high-resolution velocity model from both Vertical Seismic Profiling (VSP) and surface seismic data. The case study comes from the Permian Basin in Texas, USA. This dataset motivates and tests several new developments in methodology that enable recovery of model results that sit within multiple a priori constraint sets. These constraints are imposed through a Projected Quasi-Newton (PQN) approach, wherein the projection set is the intersection of physical property bounds and anisotropic wavenumber filtering. This enables the method to recover geologically-reasonable models while preserving the fast model convergence offered by a quasi-Newton optimization scheme like l-BFGS. In the Permian Basin example, low-frequency data from both arrays are inverted together and regularized by this projection approach. Careful choice of the constraint sets is possible without requiring tradeoff parameters as in a quadratic penalty approach to regularization. Multiple 2D FWI results are combined to produce an interpolated 3D model that is consistent with the models from migration velocity analysis and VSP processing, while offering improved resolution and illumination of features from both datasets.},
	keywords = {EAGE, VSP, waveform inversion},
	doi = {10.3997/2214-4609.201412906},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/smithyman2015EAGEcwi/smithyman2015EAGEcwi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/smithyman2015EAGEcwi/smithyman2015EAGEcwi_pres.pdf},
	author = {Brendan R. Smithyman and Bas Peters and Felix J. Herrmann}
}
@techreport {peters2015EAGErwi,
	title = {Regularizing waveform inversion by projection onto intersections of convex sets},
	number = {TR-EOAS-2015-4},
	year = {2015},
	month = {01},
	institution = {UBC},
	abstract = {A framework is proposed for regularizing the waveform inversion problem by projections onto intersections of convex sets. Multiple pieces of prior information about the geology are represented by multiple convex sets, for example limits on the velocity or minimum smoothness conditions on the model. The data-misfit is then minimized, such that the estimated model is always in the intersection of the convex sets. Therefore, it is clear what properties the estimated model will have at each iteration. This approach does not require any quadratic penalties to be used and thus avoids the known problems and limitations of those types of penalties. It is shown that by formulating waveform inversion as a constrained problem, regularization ideas such as Tikhonov regularization and gradient filtering can be incorporated into one framework. The algorithm is generally applicable, in the sense that it works with any (differentiable) objective function, several gradient and quasi-Newton based solvers and does not require significant additional computation. The method is demonstrated on the inversion of very noisy synthetic data and vertical seismic profiling field data.},
	keywords = {convex sets, regularization, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/peters2015EAGErwi/peters2015EAGErwi.html},
	author = {Bas Peters and Brendan R. Smithyman and Felix J. Herrmann}
}
@presentation {peters2015SINBADrwi,
	title = {Regularizing waveform inversion by projections onto convex sets},
	year = {2015},
	publisher = {SINBAD},
	abstract = {A framework is proposed for regularizing the waveform inversion problem by projections onto intersections of convex sets. Multiple pieces of prior information about the geology are represented by multiple convex sets, for example limits on the velocity or minimum smoothness conditions on the model. The data-misfit is then minimized, such that the estimated model is always in the intersection of the convex sets. Therefore, it is clear what properties the estimated model will have at each iteration. This approach does not require any quadratic penalties to be used and thus avoids the known problems and limitations of those types of penalties. It is shown that by formulating waveform inversion as a constrained problem, regularization ideas such as Tikhonov regularization and gradient filtering can be incorporated into one framework. The algorithm is generally applicable, in the sense that it works with any (differentiable) objective function and does not require significant additional computation. The method is demonstrated on the inversion of the 2D marine isotropic elastic synthetic seismic benchmark by Chevron using an acoustic modeling code. To highlight the effect of the projections, we apply no data pre-processing.},
	keywords = {Presentation, SINBAD, SINBADSPRING2015, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Spring/peters2015SINBADrwi/peters2015SINBADrwi.pdf},
	author = {Bas Peters and Brendan R. Smithyman and Felix J. Herrmann}
}
@techreport {peters2015SEGrwi,
	title = {Regularizing waveform inversion by projections onto convex sets {\textendash}- application to the 2D Chevron 2014 synthetic blind-test dataset},
	number = {TR-EOAS-2015-7},
	year = {2015},
	month = {06},
	institution = {UBC},
	abstract = {A framework is proposed for regularizing the waveform inversion problem by projections onto intersections of convex sets. Multiple pieces of prior information about the geology are represented by multiple convex sets, for example limits on the velocity or minimum smoothness conditions on the model. The data-misfit is then minimized, such that the estimated model is always in the intersection of the convex sets. Therefore, it is clear what properties the estimated model will have at each iteration. This approach does not require any quadratic penalties to be used and thus avoids the known problems and limitations of those types of penalties. It is shown that by formulating waveform inversion as a constrained problem, regularization ideas such as Tikhonov regularization and gradient filtering can be incorporated into one framework. The algorithm is generally applicable, in the sense that it works with any (differentiable) objective function and does not require significant additional computation. The method is demonstrated on the inversion of the 2D marine isotropic elastic synthetic seismic benchmark by Chevron using an acoustic modeling code. To highlight the effect of the projections, we apply no data pre-processing.},
	keywords = {blind-test, projection, regularization, SEG, Wavefield Reconstruction Inversion, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/peters2015SEGrwi/peters2015SEGrwi.html},
	author = {Bas Peters and Zhilong Fang and Brendan R. Smithyman and Felix J. Herrmann}
}
@conference {louboutin2015IIPFWIrwi,
	title = {Regularizing waveform inversion by projections onto convex sets},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {A framework is proposed for regularizing the waveform inversion problem by projections onto intersections of convex sets. Multiple pieces of prior information about the geology are represented by multiple convex sets, for example limits on the velocity or minimum smoothness conditions on the model. The data-misfit is then minimized, such that the estimated model is always in the intersection of the convex sets. Therefore, it is clear what properties the estimated model will have at each iteration. This approach does not require any quadratic penalties to be used and thus avoids the known problems and limitations of those types of penalties. It is shown that by formulating waveform inversion as a constrained problem, regularization ideas such as Tikhonov regularization and gradient filtering can be incorporated into one framework. The algorithm is generally applicable, in the sense that it works with any (differentiable) objective function and does not require significant additional computation. The method is demonstrated on the inversion of the 2D marine isotropic elastic synthetic seismic benchmark by Chevron using an acoustic modeling code. To highlight the effect of the projections, we apply no data pre-processing. This is joint work with Bas Peters.},
	keywords = {convex, FWI, regularization},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/louboutin2015IIPFWIrwi/louboutin2015IIPFWIrwi_pres.pdf},
	author = {Mathias Louboutin and Bas Peters and Brendan R. Smithyman and Felix J. Herrmann}
}
@presentation {peters2015SINBADFrwi,
	title = {Regularizing waveform inversion by projections onto intersections of convex sets},
	year = {2015},
	publisher = {SINBAD},
	abstract = {Common strategies to regularize waveform inversion (and other geophysical inverse problems) are adding quadratic penalty terms to the objective function or filtering the gradients used to update the model estimate. An example are penalties or filters to prevent/filter spurious high spatial frequency oscillations in the model while working with low frequency data. We present an alternative way of regularization, which works by projecting the model onto an intersection of convex sets, where each sets encodes certain desired model properties. This approach has certain theoretical and practical advantages over quadratic penalties or gradient filters. Some examples of useful convex sets in various challenging waveform inversion settings are shown on both real and synthetic data.},
	keywords = {Presentation, SINBAD, SINBADFALL2015, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/peters2015SINBADFrwi/peters2015SINBADFrwi.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/peters2015SINBADFrwi/peters2015SINBADFrwi.mov},
	author = {Bas Peters and Brendan R. Smithyman and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {dasilva2015SINBADFsss,
	title = {Scaling SINBAD software to 3-D on Yemoja},
	year = {2015},
	publisher = {SINBAD},
	abstract = {We present early results on the scalability of SINBAD{\textquoteright}s wavefield reconstruction and wave-equation based inversion technologies on Yemoja, a 17k core cluster made available to us by BG Group at SENAI CIMATEC Supercomputing Centre in Brazil.},
	keywords = {Presentation, SINBAD, SINBADFALL2015, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/dasilva2015SINBADFsss/dasilva2015SINBADFsss.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/dasilva2015SINBADFsss/dasilva2015SINBADFsss.mov},
	author = {Curt Da Silva and Haneet Wason and Mathias Louboutin and Bas Peters and Shashin Sharan and Zhilong Fang and Felix J. Herrmann}
}
@presentation {sharan2015SINBADFscu,
	title = {Source collocation using the method of Linearized Bregman},
	year = {2015},
	publisher = {SINBAD},
	abstract = {In this work, we present a method to collocate sources from seismic reflections recorded at receiver locations. We use the method of linearized Bregman. This algorithm focuses unknown sources by promoting sparsity in the {\textquotedblleft}Helmholtz domain{\textquotedblright}{\textemdash}i.e., the wavefield under the action of the the Helmholtz system{\textemdash}under the constraint of a data misfit within a particular tolerance. We extend this method to noisy measurements. We are in particular interested in situations where the noise is coherent because it is in the range of the Helmholtz equation.},
	keywords = {Presentation, SINBAD, SINBADFALL2015, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/sharan2015SINBADFscu/sharan2015SINBADFscu.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/sharan2015SINBADFscu/sharan2015SINBADFscu.mov},
	author = {Shashin Sharan and Rongrong Wang and Felix J. Herrmann}
}
@presentation {peters2014SINBADcda,
	title = {Challenges and developments arising from 2D FWI of a land VSP dataset in the Permian Basin},
	year = {2014},
	publisher = {SINBAD},
	abstract = {Full-waveform inversion was carried out to map 3D velocity structures for a site in the Permian Basin of Texas, USA. The data come from co-located surface and 3D VSP seismic surveys that share common source vibration points. This challenging on-land setting has been used as a testbed to evaluate our FWI algorithms and their effectiveness when applied to real-data problems. We discuss the challenges posed by this case study, and several new techniques and methodological refinements that have been developed and tested as a result. These include: regularization and incorporation of multiple datasets in an on-land FWI workflow; restrictions on the types of models allowed (viz., smoothness regularization) by quadratic penalty and by Projected Quasi-Newton (PQN) inversion; corrections to enable 2D FWI and recovery of 3D models; the state of ongoing work in WRI ({\textquoteleft}{\textquoteleft}Penalty Method{\textquoteright}{\textquoteright} inversion) and the handling of anisotropy.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/peters2014SINBADcda/peters2014SINBADcda.pdf},
	author = {Brendan R. Smithyman and Bas Peters and Felix J. Herrmann}
}
@techreport {smithyman2014SEGjfw,
	title = {Joint full-waveform inversion of on-land surface and VSP data from the Permian Basin},
	number = {TR-EOAS-2014-4},
	year = {2014},
	month = {04},
	institution = {UBC},
	abstract = {Full-waveform Inversion is applied to generate a high-resolution model of P-wave velocity for a site in the Permian Basin, Texas, USA. This investigation jointly inverts seismic waveforms from a surface 3-D vibroseis surface seismic survey and a co-located 3-D Vertical Seismic Profiling (VSP) survey, which shared common source Vibration Points (VPs). The resulting velocity model captures features that were not resolvable by conventional migration velocity analysis.},
	keywords = {downhole receivers, Full-waveform inversion, land, seismic, vibroseis},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/smithyman2014SEGjfw/smithyman2014SEGjfw.html},
	author = {Brendan R. Smithyman and Bas Peters and Bryan DeVault and Felix J. Herrmann}
}
@article {shahidi2013GPars,
	title = {Application of randomized sampling schemes to curvelet-based sparsity-promoting seismic data recovery},
	journal = {Geophysical Prospecting},
	volume = {61},
	number = {5},
	year = {2013},
	month = {09},
	pages = {973-997},
	abstract = {Reconstruction of seismic data is routinely used to improve the quality and resolution of seismic data from incomplete acquired seismic recordings. Curvelet-based Recovery by Sparsity-promoting Inversion, adapted from the recently-developed theory of compressive sensing, is one such kind of reconstruction, especially good for recovery of undersampled seismic data. Like traditional Fourier-based methods, it performs best when used in conjunction with randomized subsampling, which converts aliases from the usual regular periodic subsampling into easy-to-eliminate noise. By virtue of its ability to control gap size, along with the random and irregular nature of its sampling pattern, jittered (sub)sampling is one proven method that has been used successfully for the determination of geophone positions along a seismic line. In this paper, we extend jittered sampling to two-dimensional acquisition design, a more difficult problem, with both underlying Cartesian, and hexagonal grids. We also study what we term separable and non-separable two-dimensional jittered samplings. We find hexagonal jittered sampling performs better than Cartesian jittered sampling, while fully non-separable jittered sampling performs better than separable jittered sampling. Two other 2D randomized sampling methods, Poisson Disk sampling and Farthest Point sampling, both known to possess blue-noise spectra, are also shown to perform well.},
	keywords = {curvelets, Geophysical Prospecting, randomized sampling},
	doi = {10.1111/1365-2478.12050},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2013/shahidi2013GPars/shahidi2013GPars.pdf},
	author = {Reza Shahidi and Gang Tang and Jianwei Ma and Felix J. Herrmann}
}
@article {herrmann2013TLEffwi,
	title = {Frugal full-waveform inversion: from theory to a practical algorithm},
	journal = {The Leading Edge},
	volume = {32},
	number = {9},
	year = {2013},
	month = {09},
	pages = {1082-1092},
	abstract = {As conventional oil and gas fields are maturing, our profession is challenged to come up with the next-generation of more and more sophisticated exploration tools. In exploration seismology this trend has led to the emergence of wave-equation based inversion technologies such as reverse-time migration and full-waveform inversion. While significant progress has been made in wave-equation based inversion, major challenges remain in the development of robust and computationally feasible workflows that give reliable results in geophysically challenging areas that may include ultra-low shear velocity zones or high-velocity salt. Moreover, sub-salt production carries risks that needs mitigation, which raises the bar from creating sub-salt images to inverting for sub-salt overpressure.},
	keywords = {Optimization, waveform inversion},
	doi = {10.1190/tle32091082.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2013/herrmann2013ffwi/herrmann2013ffwi.html},
	author = {Felix J. Herrmann and Andrew J. Calvert and Ian Hanlon and Mostafa Javanmehri and Rajiv Kumar and Tristan van Leeuwen and Xiang Li and Brendan R. Smithyman and Eric Takam Takougang and Haneet Wason}
}
@presentation {li2013SINBADgom,
	title = {Lessons learned from Chevron Gulf of Mexico data set},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Chevron Gulf of Mexico data set is very challenging for FWI because of elastic phases, limited offset, lack of low frequencies and salt structure. To overcome these issue, we first use ray-based tomography on the hand-picked first breaks to generate initial model for FWI, and then we apply curvelet-denosing techniques to improve the poor signal-to-noise ratio of the observed data at low frequencies. Finally, Curvelet domain sparsity promoting Gauss-Newton FWI helps to suppress model space artifacts caused by elastic phases. This is joint work with Andrew J. Calvert, Ian Hanlon, Mostafa Javanmehri, Rajiv Kumar, Tristan van Leeuwen, Brendan R. Smithyman, Haneet Wason and Felix J. Herrmann},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/li2013SINBADgom/li2013SINBADgom.pdf},
	author = {Xiang Li and Andrew J. Calvert and Ian Hanlon and Mostafa Javanmehri and Rajiv Kumar and Tristan van Leeuwen and Brendan R. Smithyman and Haneet Wason and Felix J. Herrmann}
}
@presentation {smithyman2013SINBADprb,
	title = {Phase-residual based quality-control methods and techniques for mitigating cycle skips},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Most full-waveform inversion algorithms use local optimization methods to iteratively improve the numerical earth model. All of these make the implicit assumption that the the model close to the true earth to avoid cycle. In practice this may not be true. We explore two questions: 1. How do we understand and visualize the cycle skip phenomenon in order to recognize it if it exists? 2. How do we automate this quality control step and use the rich information from multiple data to mitigate cycle skips and avoid local minima?},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/smithyman2013SINBADprb/smithyman2013SINBADprb.pdf},
	author = {Brendan R. Smithyman and Felix J. Herrmann}
}
@conference {herrmann2012SEGfwi,
	title = {FWI from the West Coasts: lessons learned from "Gulf of Mexico Imaging Challenges: What Can Full Waveform Inversion Achieve?"},
	booktitle = {SEG Workshop on FWI; Las Vegas},
	year = {2012},
	publisher = {SEG},
	organization = {SEG},
	keywords = {FWI, SEG, workshop},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/herrmann2012SEGfwi/herrmann2012SEGfwi_pres.pdf},
	author = {Andrew J. Calvert and Ian Hanlon and Mostafa Javanmehri and Rajiv Kumar and Tristan van Leeuwen and Xiang Li and Brendan R. Smithyman and Eric Takam Takougang and Haneet Wason and Felix J. Herrmann}
}
@article {Friedlander11TRhdm,
	title = {Hybrid deterministic-stochastic methods for data fitting},
	journal = {SIAM Journal on Scientific Computing},
	volume = {34},
	number = {3},
	year = {2012},
	month = {01},
	pages = {A1380-A1405},
	abstract = {Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms (both deterministic and randomized) offer inexpensive iterations by sampling only subsets of the terms in the sum. These methods can make great progress initially, but often slow as they approach a solution. In contrast, full gradient methods achieve steady convergence at the expense of evaluating the full objective and gradient on each iteration. We explore hybrid methods that exhibit the benefits of both approaches. Rate of convergence analysis and numerical experiments illustrate the potential for the approach.},
	keywords = {Optimization},
	doi = {10.1137/110830629},
	author = {Michael P. Friedlander and Mark Schmidt}
}
@presentation {herrmann2012SINBADfwi,
	title = {Our findings on the Chevron benchmark dataset},
	year = {2012},
	publisher = {SINBAD},
	abstract = {During this presentation, we will review our findings working with the synthetic GOM data released as part of the post SEG workshop:"Gulf of Mexico Imaging Challenges: What Can Full Waveform Inversion Achieve?". This is joint work with Andrew J. Calvert, Ian Hanlon, Mostafa Javanmehri, Rajiv Kumar, Tristan van Leeuwen, Xiang Li, Brendan R. Smithyman, Eric Takam Takougang, and Haneet Wason.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/herrmann2012SINBADfwi/herrmann2012SINBADfwi_pres.pdf},
	author = {Andrew J. Calvert and Ian Hanlon and Mostafa Javanmehri and Rajiv Kumar and Tristan van Leeuwen and Xiang Li and Brendan R. Smithyman and Eric Takam Takougang and Haneet Wason and Felix J. Herrmann}
}
@article {mansour2012IEEETITrcs,
	title = {Recovering compressively sampled signals using partial support information},
	journal = {IEEE Transactions on Information Theory},
	volume = {58},
	number = {2},
	year = {2012},
	month = {02},
	pages = {1122-1134},
	publisher = {Department of Computer Science},
	address = {University of British Columbia, Vancouver},
	abstract = {We study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50\% of the (partial) support information is accurate, then weighted $\ell_1$ minimization is stable and robust under weaker sufficient conditions than the analogous conditions for standard $\ell_1$ minimization. Moreover, weighted $\ell_1$ minimization provides better upper bounds on the reconstruction error in terms of the measurement noise and the compressibility of the signal to be recovered. We illustrate our results with extensive numerical experiments on synthetic data and real audio and video signals.},
	keywords = {Compressive Sensing},
	doi = {10.1109/TIT.2011.2167214},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETransInformationTheory/2012/mansour2012IEEETITrcs/mansour2012IEEETITrcs.pdf},
	author = {Michael P. Friedlander and Hassan Mansour and Rayan Saab and Ozgur Yilmaz}
}
@conference {vanleeuwen2011AMPhsdmwi,
	title = {A hybrid stocahstic-deterministic method for waveform inversion},
	booktitle = {AMP},
	year = {2011},
	note = {Presented at AMP Medical and Seismic Imaging, 2011, Vancouver BC},
	month = {07},
	publisher = {WAVES 2011},
	organization = {WAVES 2011},
	abstract = {A lot of seismic and medical imaging problems can be written as a least-squares data- fitting problem. In particular, we consider the case of multi-experiment data, where the data consists of a large number of "independent" measurements. Solving the inverse problem then involves repeatedly forward modeling the data for each of these experiments. In case the number of experiments is large and the modeling kernel expensive to apply, such an approach may be prohibitively expensive. We review techniques from stochastic optimization which aim at dramatically reducing the number of experiments that need to be modeled at each iteration. This reduction is typically achieved by randomly subsampling the data. Special care needs to be taken in the optimization to deal with the stochasticity that is introduced in this way.},
	keywords = {Presentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICIAM/2011/vanleeuwen2011AMPhsdmwi/vanleeuwen2011AMPhsdmwi.pdf},
	author = {Tristan van Leeuwen and Mark Schmidt and Michael P. Friedlander and Felix J. Herrmann}
}
@conference {vanleeuwen2011EAGEhsdomwi,
	title = {A hybrid stochastic-deterministic optimization method for waveform inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2011},
	month = {05},
	abstract = {Present-day high quality 3D acquisition can give us lower frequencies and longer offsets with which to invert. However, the computational costs involved in handling this data explosion are tremendous. Therefore, recent developments in full-waveform inversion have been geared towards reducing the computational costs involved. A key aspect of several approaches that have been proposed is a dramatic reduction in the number of sources used in each iteration. A reduction in the number of sources directly translates to less PDE-solves and hence a lower computational cost. Recent attention has been drawn towards reducing the sources by randomly combining the sources in to a few supershots, but other strategies are also possible. In all cases, the full data misfit, which involves all the sequential sources, is replaced by a reduced misfit that is much cheaper to evaluate because it involves only a small number of sources (batchsize). The batchsize controls the accuracy with which the reduced misfit approximates the full misfit. The optimization of such an inaccurate, or noisy, misfit is the topic of stochastic optimization. In this paper, we propose an optimization strategy that borrows ideas from the field of stochastic optimization. The main idea is that in the early stage of the optimization, far from the true model, we do not need a very accurate misfit. The strategy consists of gradually increasing the batchsize as the iterations proceed. We test the proposed strategy on a synthetic dataset. We achieve a very reasonable inversion result at the cost of roughly 13 evaluations of the full misfit. We observe a speed-up of roughly a factor 20.},
	keywords = {EAGE, Full-waveform inversion, Optimization, Presentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/vanleeuwen11EAGEhsdomwi/vanleeuwen11EAGEhsdomwi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/vanleeuwen11EAGEhsdomwi/vanleeuwen11EAGEhsdomwi_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=50341},
	author = {Tristan van Leeuwen and Felix J. Herrmann and Mark Schmidt and Michael P. Friedlander}
}
@conference {frijlink2010EAGEcos,
	title = {Comparison of standard adaptive subtraction and primary-multiple separation in the curvelet domain},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2010},
	month = {06},
	abstract = {In recent years, data-driven multiple prediction methods and wavefield extrapolation methods have proven to be powerful methods to attenuate multiples from data acquired in complex 3-D geologic environments. These methods make use of a two-stage approach, where first the multiples (surface-related and / or internal) multiples are predicted before they are subtracted from the original input data in an adaptively. The quality of these predicted multiples often raises high expectations for the adaptive subtraction techniques, but for various reasons these expectations are not always met in practice. Standard adaptive subtraction methods use the well-known minimum energy criterion, stating that the total energy after optimal multiple attenuation should be minimal. When primaries and multiples interfere, the minimum energy criterion is no longer appropriate. Also, when multiples of different orders interfere, adaptive energy minimization will lead to a compromise between different amplitudes corrections for the different orders of multiples. This paper investigates the performance of two multiple subtraction schemes for a real data set that exhibits both interference problems. Results from an adaptive subtraction in the real curvelet domain, separating primaries and multiples, are compared to those obtained using a more conventional adaptive subtraction method in the spatial domain.},
	keywords = {EAGE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2010/frijlink10EAGEcos/frijlink10EAGEcos.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=39875},
	author = {M. O. Frijlink and Reza Shahidi and Felix J. Herrmann and R. G. van Borselen}
}
@presentation {saab2010SINBADcsk,
	title = {Compressed sensing using Kronecker products},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/saab2010SINBADcsk/saab2010SINBADcsk_pres.pdf},
	author = {Rayan Saab}
}
@presentation {schmidt2010SINBADhsd,
	title = {Hybrid stochastic-deterministic methods},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/schmidt2010SINBADhsd/schmidt2010SINBADhsd_pres.pdf},
	author = {Mark Schmidt}
}
@article {saab2008ACHAsrb,
	title = {Sparse recovery by non-convex optimization - instance optimality},
	journal = {Applied and Computational Harmonic Analysis},
	volume = {29},
	number = {1},
	year = {2010},
	month = {07},
	pages = {30-48},
	abstract = {In this note, we address the theoretical properties of $\Delta_p$, a class of compressed sensing decoders that rely on $l^p$ minimization with $p \in (0,1)$ to recover estimates of sparse and compressible signals from incomplete and inaccurate measurements. In particular, we extend the results of Cand{\textquoteleft}es, Romberg and Tao [3] and Wojtaszczyk [30] regarding the decoder $\Delta_1$, based on $\ell^1$ minimization, to $Δp$ with $p \in (0,1)$. Our results are two-fold. First, we show that under certain sufficient conditions that are weaker than the analogous sufficient conditions for $\Delta_1$ the decoders $\Delta_p$ are robust to noise and stable in the sense that they are $(2,p)$ instance optimal. Second, we extend the results of Wojtaszczyk to show that, like $\Delta_1$, the decoders $\Delta_p$ are (2,2) instance optimal in probability provided the measurement matrix is drawn from an appropriate distribution. While the extension of the results of [3] to the setting where $p \in (0,1)$ is straightforward, the extension of the instance optimality in probability result of [30] is non-trivial. In particular, we need to prove that the $LQ_1$ property, introduced in [30], and shown to hold for Gaussian matrices and matrices whose columns are drawn uniformly from the sphere, generalizes to an $LQ_p$ property for the same classes of matrices. Our proof is based on a result by Gordon and Kalton [18] about the Banach-Mazur distances of p-convex bodies to their convex hulls.},
	keywords = {Compressive Sensing, non-convex},
	doi = {10.1016/j.acha.2009.08.002},
	url = {http://www.sciencedirect.com/science/article/pii/S1063520309000864},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/ACHA/2010/saab2008ACHAsrb/saab2008ACHAsrb.pdf},
	author = {Rayan Saab and Ozgur Yilmaz}
}
@conference {herrmann09EAGEbnrs,
	title = {Beating Nyquist by randomized sampling},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2009},
	note = {Presented at the EAGE (workshop), Amsterdam},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2009/herrmann09EAGEbnrs/herrmann09EAGEbnrs.pdf},
	author = {Felix J. Herrmann and Gang Tang and Reza Shahidi and Gilles Hennenfent and Tim T.Y. Lin}
}
@conference {shahidi2009SEGcmf,
	title = {Curvelet-domain matched filtering with frequency-domain regularization},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {28},
	year = {2009},
	month = {10},
	pages = {3645-3649},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In Herrmann et al. (2008), it is shown that zero-order pseudodifferential operators, which model the migration-demigration operator and the operator mapping the predicted multiples to the true multiples, can be represented by a diagonal weighting in the curvelet domain. In that paper, a smoothness constraint was introduced in the phase space of the operator in order to regularize the solution to make it unique. In this paper, we use recent results in Demanet and Ying (2008) on the discrete symbol calculus to impose a further smoothness constraint, this time in the frequency domain. It is found that with this additional constraint, faster convergence is realized. Results on a synthetic pseudodifferential operator as well as on an example of primary-multiple separation in seismic data are included, comparing the model with and without the new smoothness constraint, from which it is found that results of improved quality are also obtained.},
	keywords = {Presentation, SEG},
	doi = {10.1190/1.3255624},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2009/shahidi09SEGcmf/shahidi09segcmf.pdf},
	author = {Reza Shahidi and Felix J. Herrmann}
}
@techreport {tang09TRdtr,
	title = {Design of two-dimensional randomized sampling schemes for curvelet-based sparsity-promoting seismic data recovery},
	number = {TR-EOAS-2009-3},
	year = {2009},
	institution = {UBC Earth and Ocean Sciences Department},
	abstract = {The tasks of sampling, compression and reconstruction are very common and often necessary in seismic data processing due to the large size of seismic data. Curvelet-based Recovery by Sparsity-promoting Inversion, motivated by the newly developed theory of compressive sensing, is among the best recovery strategies for seismic data. The incomplete data input to this curvelet-based recovery is determined by randomized sampling of the original complete data. Unlike usual regular undersampling, randomized sampling can convert aliases to easy-to-eliminate noise, thus facilitating the process of reconstruction of the complete data from the incomplete data. Randomized sampling methods such as jittered sampling have been developed in the past that are suitable for curvelet-based recovery, however most have only been applied to sampling in one dimension. Considering that seismic datasets are usually higher dimensional and extremely large, in the present paper, we extend the 1D version of jittered sampling to two dimensions, both with underlying Cartesian and hexagonal grids. We also study separable and non-separable two dimensional jittered sampling, the former referring to the Kronecker product of two one-dimensional jittered samplings. These different categories of jittered sampling are compared against one another in terms of signal-to-noise ratio and visual quality, from which we find that jittered hexagonal sampling is better than jittered Cartesian sampling, while fully non-separable jittered sampling is better than separable sampling. Because in the image processing and computer graphics literature, sampling patterns with blue-noise spectra are found to be ideal to avoid aliasing, we also introduce two other randomized sampling methods, possessing sampling spectra with beneficial blue noise characteristics, Poisson Disk sampling and Farthest Point sampling. We compare these methods, and apply the introduced sampling methodologies to higher dimensional curvelet-based reconstruction. These sampling schemes are shown to lead to better results from CRSI compared to the other more traditional sampling protocols, e.g. regular subsampling.},
	url = {https://slim.gatech.edu/Publications/Public/Journals/2009/tang09TRdtr/tang09TRdtr.pdf},
	author = {Gang Tang and Reza Shahidi and Jianwei Ma}
}
@conference {tang2009SEGhdb,
	title = {Higher dimensional blue-noise sampling schemes for curvelet-based seismic data recovery},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {28},
	year = {2009},
	month = {10},
	pages = {191-195},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In combination with compressive sensing, a successful reconstruction scheme called Curvelet-based Recovery by Sparsity-promoting Inversion (CRSI) has been developed, and has proven to be useful for seismic data processing. One of the most important issues for CRSI is the sampling scheme, which can greatly affect the quality of reconstruction. Unlike usual regular undersampling, stochastic sampling can convert aliases to easy-to-eliminate noise. Some stochastic sampling methods have been developed for CRSI, e.g. jittered sampling, however most have only been applied to 1D sampling along a line. Seismic datasets are usually higher dimensional and very large, thus it is desirable and often necessary to develop higher dimensional sampling methods to deal with these data. For dimensions higher than one, few results have been reported, except uniform random sampling, which does not perform well. In the present paper, we explore 2D sampling methodologies for curvelet-based reconstruction, possessing sampling spectra with blue noise characteristics, such as Poisson Disk sampling, Farthest Point Sampling, and the 2D extension of jittered sampling. These sampling methods are shown to lead to better recovery and results are compared to the other more traditional sampling protocols.},
	keywords = {Presentation, SEG},
	doi = {10.1190/1.3255230},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2009/tang09SEGhdb/tang09SEGhdb.pdf},
	author = {Gang Tang and Reza Shahidi and Felix J. Herrmann and Jianwei Ma}
}
@conference {vandenberg2009SLIMocf,
	title = {Optimizing costly functions with simple constraints: a limited-memory projected Quasi-Newton algorithm},
	booktitle = {SLIM},
	series = {Twelfth International Conference on Artificial Intelligence and Statistics},
	volume = {12},
	year = {2009},
	month = {04},
	abstract = {An optimization algorithm for minimizing a smooth function over a convex set is described. Each iteration of the method computes a descent direction by minimizing, over the original constraints, a diagonal-plus low-rank quadratic approximation to the function. The quadratic approximation is constructed using a limited-memory quasi-Newton update. The method is suitable for large-scale problems where evaluation of the function is substan- tially more expensive than projection onto the constraint set. Numerical experiments on one-norm regularized test problems indicate that the proposed method is competitve with state-of-the-art methods such as bound-constrained L-BFGS and orthant-wise descent. We further show that the method generalizes to a wide class of problems, and substantially improves on state-of-the-art methods for problems such as learning the structure of Gaussian graphi- cal models (involving positive-definite matrix constraints) and Markov random fields (involving second-order cone constraints).},
	keywords = {SLIM},
	url = {http://www.cs.ubc.ca/ mpf/papers/SchmidtBergFriedMurph09.pdf},
	author = {Ewout van den Berg and Mark Schmidt and Michael P. Friedlander and K. Murphy}
}
@conference {saab2009SAMPTAnccs,
	title = {A short note on non-convex compressed sensing},
	booktitle = {SAMPTA technical program},
	year = {2009},
	publisher = {SAMPTA},
	organization = {SAMPTA},
	abstract = {In this note, we summarize the results we recently proved in\citeSY08 on the theoretical performance guarantees of the decoders $\Delta_p$. These decoders rely on $\ell^p$ minimization with $p {\i}n (0,1)$ to recover estimates of sparse and compressible signals from incomplete and inaccurate measurements. Our guarantees generalize the results of \citeCRT05 and \citeWojtaszczyk08 about decoding by $\ell_p$ minimization with $p = 1$, to the setting where $p {\i}n (0,1)$ and are obtained under weaker sufficient conditions. We also present novel extensions of our results in \citeSY08 that follow from the recent work of DeVore et al. in \citeDPW08. Finally, we show some insightful numerical experiments displaying the trade-off in the choice of $p \in (0,1]$ depending on certain properties of the input signal.},
	keywords = {Presentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SAMPTA/2009/saab09SAMPTAnccs/saab09SAMPTAnccs.pdf},
	author = {Rayan Saab and Ozgur Yilmaz}
}
@article {vandenberg2009ACMstf,
	title = {Sparco: a testing framework for sparse reconstruction},
	journal = {ACM Transactions on Mathematical Software},
	volume = {35},
	number = {4},
	year = {2009},
	month = {02},
	pages = {1-16},
	abstract = {Sparco is a framework for testing and benchmarking algorithms for sparse reconstruction. It includes a large collection of sparse reconstruction problems drawn from the imaging, compressed sensing, and geophysics literature. Sparco is also a framework for implementing new test problems and can be used as a tool for reproducible research. Sparco is implemented entirely in Matlab, and is released as open-source software under the GNU Public License.},
	keywords = {compressed sensing, linear operators, Sparse recovery},
	url = {http://doi.acm.org/10.1145/1462173.1462178},
	author = {Ewout van den Berg and Michael P. Friedlander and Gilles Hennenfent and Felix J. Herrmann and Rayan Saab and Ozgur Yilmaz}
}
@conference {friedlander2008WCOMasm,
	title = {Active-set methods for basis pursuit},
	booktitle = {WCOM},
	year = {2008},
	month = {07},
	publisher = {West Coast Opitmization Meeting (WCOM)},
	organization = {West Coast Opitmization Meeting (WCOM)},
	abstract = {Many imaging and compressed sensing applications seek sparse solutions to large under-determined least-squares problems. The basis pursuit (BP) approach minimizes the 1-norm of the solution, and the BP denoising (BPDN) approach balances it against the least-squares fit. The duals of these problems are conventional linear and quadratic programs. We introduce a modified parameterization of the BPDN problem and explore the effectiveness of active-set methods for solving its dual. Our basic algorithm for the BP dual unifies several existing algorithms and is applicable to large-scale examples.},
	url = {http://www.cs.ubc.ca/ mpf/public/mpf08siopt.pdf},
	author = {Michael P. Friedlander and M. A. Saunders}
}
@article {wang2008GEOPbws,
	title = {Bayesian wavefield separation by transform-domain sparsity promotion},
	journal = {Geophysics},
	volume = {73},
	number = {5},
	year = {2008},
	month = {07},
	pages = {1-6},
	abstract = {Successful removal of coherent noise sources greatly determines the quality of seismic imaging. Major advances were made in this direction, e.g., Surface-Related Multiple Elimination (SRME) and interferometric ground-roll removal. Still, moderate phase, timing, amplitude errors and clutter in the predicted signal components can be detrimental. Adopting a Bayesian approach along with the assumption of approximate curvelet-domain independence of the to-be-separated signal components, we construct an iterative algorithm that takes the predictions produced by for example SRME as input and separates these components in a robust fashion. In addition, the proposed algorithm controls the energy mismatch between the separated and predicted components. Such a control, which was lacking in earlier curvelet-domain formulations, produces improved results for primary-multiple separation on both synthetic and real data.},
	keywords = {curvelet transform, Geophysics, Optimization, Processing, SLIM},
	doi = {10.1190/1.2952571},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/wang08GEObws/wang08GEObws.pdf},
	html_version = {https://slim.gatech.edu/Publications/Public/Journals/2008/wang08TRbss/paper_html/paper.html},
	author = {Deli Wang and Rayan Saab and Ozgur Yilmaz and Felix J. Herrmann}
}
@conference {saab2008SINBADcps,
	title = {Curvelet-based primary-multiple separation from a Bayesian perspective},
	booktitle = {SINBAD 2008},
	year = {2008},
	abstract = {We present a novel primary-multiple separation scheme which makes use of the sparsity of both primaries and multiples in a transform domain, such as the curvelet transform, to provide estimates of each. The proposed algorithm utilizes seismic data as well as the output of a preliminary step that provides (possibly) erroneous predictions of the multiples. The algorithm separates the signal components, i.e., the primaries and multiples, by solving an optimization problem that assumes noisy input data and can be derived from a Bayesian perspective. More precisely, the optimization problem can be arrived at via an assumption of a weighted Laplacian distribution for the primary and multiple coefficients in the transform domain and of white Gaussian noise contaminating both the seismic data and the preliminary prediction of the multiples, which both serve as input to the algorithm.},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/saab2008SINBADcps/saab2008SINBADcp.pdf},
	author = {Rayan Saab}
}
@techreport {vandenberg08gsv,
	title = {Group sparsity via linear-time projection},
	number = {TR-2008-09},
	year = {2008},
	month = {06},
	institution = {UBC - Department of Computer Science},
	abstract = {We present an efficient spectral projected-gradient algorithm for optimization subject to a group one-norm constraint. Our approach is based on a novel linear-time algorithm for Euclidean projection onto the one- and group one-norm constraints. Numerical experiments on large data sets suggest that the proposed method is substantially more efficient and scalable than existing methods.},
	keywords = {Optimization, SLIM},
	url = {http://www.optimization-online.org/DB_FILE/2008/07/2056.pdf},
	author = {Ewout van den Berg and Mark Schmidt and Michael P. Friedlander and K. Murphy}
}
@conference {wang2008SINBADrri,
	title = {Recent results in curvelet-based primary-multiple separation},
	booktitle = {SINBAD 2008},
	year = {2008},
	abstract = {We present a nonlinear curvelet-based sparsity-promoting formulation for the primary-multiple separation problem. We show that these coherent signal components can be separated robustly by explicitly exploiting the locality of curvelets in phase space (space-spatial frequency plane) and their ability to compress data volumes that contain wavefronts. This work is an extension of earlier results and the presented algorithms are shown to be stable under noise and moderately erroneous multiple predictions.},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/wang2008SINBADrri/wang2008SINBADrri.pdf},
	author = {Deli Wang and Rayan Saab and Ozgur Yilmaz and Felix J. Herrmann}
}
@article {herrmann2008ACHAsac,
	title = {Sparsity- and continuity-promoting seismic image recovery with curvelet frames},
	journal = {Applied and Computational Harmonic Analysis},
	volume = {24},
	number = {2},
	year = {2008},
	month = {03},
	pages = {150-173},
	abstract = {A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. We observe that curvelets, as a directional frame expansion, lead to sparsity of seismic images and exhibit invariance under the normal operator of the linearized imaging problem. Based on this observation we derive a method for stable recovery of the migration amplitudes from noisy data. The method corrects the amplitudes during a post-processing step after migration, such that the main additional cost is one ap- plication of the normal operator, i.e. a modeling followed by a migration. Asymptotically this normal operator corresponds to a pseudodifferential operator, for which a convenient diagonal approximation in the curvelet domain is derived, including a bound for its error and a method for the estimation of the diagonal from a compound operator consisting of discrete implementations for the scattering operator and its adjoint the migration operator. The solution is formulated as a nonlinear optimization problem where sparsity in the curvelet domain as well as continuity along the imaged reflectors are jointly promoted. To enhance sparsity, the $ell_1$-norm on the curvelet coefficients is minimized, while continuity is promoted by minimizing an anisotropic diffusion norm on the image. The performance of the recovery scheme is evaluated with a time-reversed {\textquoteright}wave-equation{\textquoteright} migration code on synthetic datasets, including the complex SEG/EAGE AA salt model.},
	keywords = {curvelet transform, Imaging, Processing, SLIM},
	doi = {10.1016/j.acha.2007.06.007},
	url = {https://slim.gatech.edu/Publications/Public/Journals/ACHA/2008/herrmann2008ACHAsac/herrmann2008ACHAsac.pdf},
	author = {Felix J. Herrmann and Peyman P. Moghaddam and Christiaan C. Stolk}
}
@conference {saab2008ICASSPssa,
	title = {Stable sparse approximations via nonconvex optimization},
	booktitle = {ICASSP},
	year = {2008},
	publisher = {ICASSP},
	organization = {ICASSP},
	abstract = {We present theoretical results pertaining to the ability of lp minimization to recover sparse and compressible signals from incomplete and noisy measurements. In particular, we extend the results of Cande{\textquoteleft}s, Romberg and Tao [1] to the p < 1 case. Our results indicate that depending on the restricted isometry constants (see, e.g.,[2] and [3]) and the noise level, lp minimization with certain values of p < 1 provides better theoretical guarantees in terms of stability and robustness than l1 minimization does. This is especially true when the restricted isometry constants are relatively large.},
	keywords = {ICASSP},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICASSP/2008/saab08ICASSPssa/saab08ICASSPssa.pdf},
	author = {Rayan Saab and Rick Chartrand and Ozgur Yilmaz}
}
@conference {saab2007SEGcbp,
	title = {Curvelet-based primary-multiple separation from a Bayesian perspective},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {26},
	year = {2007},
	pages = {2510-2514},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In this abstract, we present a novel primary-multiple separation scheme which makes use of the sparsity of both primaries and multiples in a transform domain, such as the curvelet transform, to provide estimates of each. The proposed algorithm utilizes seismic data as well as the output of a preliminary step that provides (possibly) erroneous predictions of the multiples. The algorithm separates the signal components, i.e., the primaries and multiples, by solving an optimization problem that assumes noisy input data and can be derived from a Bayesian perspective. More precisely, the optimization problem can be arrived at via an assumption of a weighted Laplacian distribution for the primary and multiple coefficients in the transform domain and of white Gaussian noise contaminating both the seismic data and the preliminary prediction of the multiples, which both serve as input to the algorithm. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2792988},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/saab07SEGcbp/saab07SEGcbp.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/saab07SEGcbp/saab07SEGcbp_pres.pdf},
	author = {Rayan Saab and Deli Wang and Ozgur Yilmaz and Felix J. Herrmann}
}
@article {friedlander2007TASdtd,
	title = {Discussion: the Dantzig selector: statistical estimation when p is much larger than n},
	journal = {The Annals of Statistics},
	volume = {35},
	number = {6},
	year = {2007},
	month = {03},
	pages = {2385-2391},
	keywords = {dantzig, SLIM, statistics},
	doi = {10.1214/009053607000000479},
	author = {Michael P. Friedlander and M. A. Saunders}
}
@conference {moghaddam2007CSEGmar,
	title = {Migration amplitude recovery using curvelets},
	booktitle = {CSEG Annual Conference Proceedings},
	year = {2007},
	month = {05},
	publisher = {CSEG},
	organization = {CSEG},
	abstract = {In this paper, we recover the amplitude of a seismic image by approximating the normal operator and subsequently inverting it. Normal operator (migration followed by modeling) is an example of pseudo-differential. curvelets are proven to be invariant under the action of pseudo-differential operators under certain conditions. Subsequently, curvelets are forming as eigen-vectors for such an operator. We propose a seismic amplitude recovery method that employs an eigen-value decomposition for normal operator using curvelets as eigen-vectors and to be estimated eigenvalues. A post-stack reverse-time, wave-equation migration is used for evaluation of the proposed method.},
	keywords = {SLIM},
	url = {http://cseg.ca/assets/files/resources/abstracts/2007/168S0131.pdf},
	author = {Peyman P. Moghaddam and Felix J. Herrmann and Christiaan C. Stolk}
}
@conference {sastry2007SINBADnor,
	title = {Norm-one recovery from irregular sampled data},
	booktitle = {SINBAD 2007},
	year = {2007},
	abstract = {Seismic traces are sampled irregularly and insufficiently due to practical and economical limitations. The use of such data in seismic imaging results in image artifacts and poor spatial resolution. Therefore, before being used, the measurements are to be interpolated onto a regular grid. One of the methods achieving this objective is based on the Fourier reconstruction, which deals with the under-determined system of equations. The recent pursuit techniques (namely, basis pursuit, matching pursuit etc) admit certain promising features such as faster and simpler implementation even in large scale settings. The presentation discusses the application of the pursuit algorithms to the Fourier-based interpolation problem for the signals that have sparse Fourier spectra. In particular, the objective of the presentation includes: 1). studying the performance of the algorithm if, and how far, the measurement coordinates can be shifted from uniform distribution on the continuous interval. 2). studying what could be the allowable misplacement in the measurement coordinates that does not alter the quality of the reconstruction process},
	keywords = {Presentation, SINBAD, SLIM},
	author = {Challa S. Sastry}
}
@conference {wang2007SEGrri,
	title = {Recent results in curvelet-based primary-multiple separation: application to real data},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {26},
	year = {2007},
	pages = {2500-2504},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In this abstract, we present a nonlinear curvelet-based sparsity-promoting formulation for the primary-multiple separation problem. We show that these coherent signal components can be separated robustly by explicitly exploting the locality of curvelets in phase space (space-spatial frequency plane) and their ability to compress data volumes that contain wavefronts. This work is an extension of earlier results and the presented algorithms are shown to be stable under noise and moderately erroneous multiple predictions. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2792986},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/wang07SEGrri/wang07SEGrri.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/wang07SEGrri/wang07SEGrri_pres.pdf},
	author = {Deli Wang and Rayan Saab and Ozgur Yilmaz and Felix J. Herrmann}
}
@conference {moghaddam2007SEGrsi,
	title = {Robust seismic-images amplitude recovery using curvelets},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {26},
	year = {2007},
	pages = {2225-2229},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In this paper, we recover the amplitude of a seismic image by approximating the normal (demigration-migration) operator. In this approximation, we make use of the property that curvelets remain invariant under the action of the normal operator. We propose a seismic amplitude recovery method that employs an eigenvalue like decomposition for the normal operator using curvelets as eigen-vectors. Subsequently, we propose an approximate non-linear singularity-preserving solution to the least-squares seismic imaging problem with sparseness in the curvelet domain and spatial continuity constraints. Our method is tested with a reverse-time {\textquoteleft}wave-equation{\textquoteright} migration code simulating the acoustic wave equation on the SEG-AA salt model. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2792928},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/moghaddam07SEGrsi/moghaddam07SEGrsi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/moghaddam07SEGrsi/moghaddam07SEGrsi_pres.pdf},
	author = {Peyman P. Moghaddam and Felix J. Herrmann and Christiaan C. Stolk}
}
@conference {moghaddam2007EAGEsar,
	title = {Seismic amplitude recovery with curvelets},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2007},
	month = {06},
	abstract = {A non-linear singularity-preserving solution to the least-squares seismic imaging problem with sparseness and continuity constraints is proposed. The applied formalism explores curvelets as a directional frame that, by their sparsity on the image, and their invariance under the imaging operators, allows for a stable recovery of the amplitudes. Our method is based on the estimation of the normal operator in the form of an {\textquoteright}eigenvalue{\textquoteright} decompsoition with curvelets as the {\textquoteright}eigenvectors{\textquoteright}. Subsequently, we propose an inversion method that derives from estimation of the normal operator and is formulated as a convex optimization problem. Sparsity in the curvelet domain as well as continuity along the reflectors in the image domain are promoted as part of this optimization. Our method is tested with a reverse-time {\textquoteright}wave-equation{\textquoteright} migration code simulating the acoustic wave equation.},
	keywords = {EAGE, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/moghaddam07EAGEsar/moghaddam07EAGEsar.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=6935},
	author = {Peyman P. Moghaddam and Felix J. Herrmann and Christiaan C. Stolk}
}
@conference {challa2007EAGEsrf,
	title = {Signal reconstruction from incomplete and misplaced measurements},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2007},
	month = {06},
	abstract = {Constrained by practical and economical considerations, one often uses seismic data with missing traces. The use of such data results in image artifacts and poor spatial resolution. Sometimes due to practical limitations, measurements may be available on a perturbed grid, instead of on the designated grid. Due to algorithmic requirements, when such measurements are viewed as those on the designated grid, the recovery procedures may result in additional artifacts. This paper interpolates incomplete data onto regular grid via the Fourier domain, using a recently developed greedy algorithm. The basic objective is to study experimentally as to what could be the size of the perturbation in measurement coordinates that allows for the measurements on the perturbed grid to be considered as on the designated grid for faithful recovery. Our experimental work shows that for compressible signals, a uniformly distributed perturbation can be offset with slightly more number of measurements.},
	keywords = {EAGE, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/challa07EAGEsrf/challa07EAGEsrf.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=6917},
	author = {Challa S. Sastry and Gilles Hennenfent and Felix J. Herrmann}
}
@conference {moghaddam2007CSEGsac,
	title = {Sparsity and continuity enhancing seismic imaging},
	booktitle = {CSEG Annual Conference Proceedings},
	year = {2007},
	month = {05},
	publisher = {CSEG},
	organization = {CSEG},
	abstract = {A non-linear singularity-preserving solution to the least-squares seismic imaging problem with sparseness and continuity constraints is proposed. The applied formalism explores curvelets as a directional frame that, by their sparsity on the image, and their invariance under the imaging operators, allows for a stable recovery of the amplitudes. Our method is based on the estimation of the normal operator in the form of an {\textquoteright}eigenvalue{\textquoteright} decompsoition with curvelets as the eigenvectors{\textquoteright}. Subsequently, we propose an inversion method that derives from estimation of the normal operator and is formulated as a convex optimization problem. Sparsity in the curvelet domain as well as continuity along the reflectors in the image domain are promoted as part of this optimization. Our method is tested with a reverse-time {\textquoteright}wave-equation{\textquoteright} migration code simulating the acoustic wave equation.},
	keywords = {SLIM},
	url = {http://cseg.ca/assets/files/resources/abstracts/2007/091S0130.pdf},
	author = {Peyman P. Moghaddam and Felix J. Herrmann and Christiaan C. Stolk}
}
@conference {sastry2007SINBADrfu,
	title = {Recovery from unstructured data},
	booktitle = {SINBAD 2006},
	year = {2006},
	keywords = {Presentation, SINBAD, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/sastry2007SINBADrfu/sastry2007SINBADrfu.pdf},
	author = {Challa S. Sastry and Gilles Hennenfent and Felix J. Herrmann}
}
