@conference {gahlot2025ML4SEISMICmrm,
	title = {Mitigating Rock-Physics Model Misspecification in Digital Shadows via Amortized Bayesian Inference},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {Digital shadows for subsurface monitoring rely on simulation-based inference to map seismic observations to evolving reservoir states. However, when the simulations are generated using simplified or different rock physics models than those governing the observed data, model misspecification leads to biased posterior estimates and degraded uncertainty quantification. We address this challenge through Bayesian frameworks including rock-physics marginalization and a context-aware amortized inference using conditional normalizing flows. The framework learns a mapping from seismic responses to pressure and saturation while accounting for variability across different randomly drawn models for the rock-physics. To enhance sensitivity to fluid and stress effects, we also incorporate pressure-dependent rock physics into the seismic forward model and perform inference in the Radon domain of Common Image Gathers (CIGs) instead of conventional RTM images. Because fluids exhibit distinct angle-dependent signatures in AVA responses, Radon-transformed CIGs are expected to provide improved separation between pressure and saturation effects, leading to more accurate and physically consistent state estimates. Thus, it enables an uncertainty-aware, physics-informed digital shadows under rock-physics model mismatch.},
	keywords = {Amortized Variational Inference, Bayesian inference, CIG, conditional normalizing flows, data assimilation, deep learning, digital twin, experimental design, GCS, Imaging, Inverse problems, ML4SEISMIC, permeability, reservoir simulation, rock physics, RTM, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/gahlot2025ML4SEISMICmrm},
	author = {Abhinav Prakash Gahlot and Ipsita Bhar and Felix J. Herrmann}
}
@conference {cirakman2025ML4SEISMICpss,
	title = {Multiscale Wavelet Score-based Posterior Approximations for Seismic Inversion},
	booktitle = {ML4SEISMIC Partners Meeting},
	year = {2025},
	month = {11},
	abstract = {We present a cascaded conditional wavelet score{\textendash}based posterior surrogate (CWSGM) for seismic inversion that generates samples of subsurface velocity fields conditioned on physics-derived summaries (e.g., RTM images). Through multi-scale wavelet-based whitening, we specifically address ill-conditioning of the velocity model{\textquoteright}s covariance (due to its fractal-like 1/f power spectrum), whose long range correlations hamper training neural networks to approximate the score function. This strategy improves the conditioning of the score-learning problem and accelerates both training and sampling. Experiments on the North Sea BG Model demonstrate that CWSGM accurately captures long-range geological correlations while reducing GPU memory usage by approximately 50\% and sampling time by 73\% compared to a single-scale vanilla score model. Overall, our approach enables efficient multi-scale generation of subsurface velocities at lower computational cost and provides a foundation for exploring alternative multiscale transforms that are more optimally aligned with seismic observations.},
	keywords = {Bayesian inference, deep learning, generative model, Imaging, Inverse problems, ML4SEISMIC, power-scaling, RTM, score, SLIM, Summary Statistics, Uncertainty quantification, WISE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2025/cirakman2025ML4SEISMICpss},
	author = {Ege Cirakman and Huseyin Tuna Erdinc 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 {li2023ML4SEISMICmci,
	title = {Maximizing CO2 injectivity within fracture pressure},
	year = {2023},
	month = {11},
	abstract = {In geological carbon storage projects, optimizing CO2 injection strategies is paramount to enhance storage efficiency and prevent leakage. The objective is to maximize the CO2 injection volume without surpassing the fracture pressure. Traditional adjoint-based approaches necessitate extensive numerical simulations, leading to significant computational overhead. To circumvent this challenge, we introduce an optimization framework based on physics-informed deep convolutional neural networks. Trained on different permeability slices, our model can rapidly predict the maximal CO2 injection volume for new permeability fields in real-time.},
	keywords = {CCS, ML4SEISMIC, Optimization, reservoir simulation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2023/li2023ML4SEISMICmci},
	author = {Haoyun Li and Ziyi Yin and Olav M{\o}yner and Felix J. Herrmann}
}
@article {grady2022SCtll,
	title = {Model-Parallel Fourier Neural Operators as Learned Surrogates for Large-Scale Parametric PDEs},
	journal = {Computers \& Geosciences},
	volume = {178},
	year = {2023},
	note = {(Computers and Geosciences)},
	month = {07},
	pages = {105402},
	abstract = {Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep learning approaches. Once trained, FNOs can achieve speed-ups of multiple orders of magnitude over conventional numerical PDE solvers. However, due to the high dimensionality of their input data and network weights, FNOs have so far only been applied to two-dimensional or small three-dimensional problems. To remove this limited problem-size barrier, we propose a model-parallel version of FNOs based on domain-decomposition of both the input data and network weights. We demonstrate that our model-parallel FNO is able to predict time-varying PDE solutions of over 2.6 billion variables on Perlmutter using up to 512 A100 GPUs and show an example of training a distributed FNO on the Azure cloud for simulating multiphase CO2 dynamics in the Earth{\textquoteright}s subsurface.},
	keywords = {CCS, Computers and Geosciences, deep learning, Fourier neural operators, HPC, large-scale, Model Parallelism, Multiphase Flow, Operator Learning},
	doi = {10.1016/j.cageo.2023.105402},
	url = {https://slim.gatech.edu/Publications/Public/Journals/ComputersAndGeosciences/2023/grady2022SCtll/grady2022SCtll.pdf},
	software = {https://github.com/slimgroup/dfno},
	author = {Thomas J. Grady II and Rishi Khan and Mathias Louboutin and Ziyi Yin and Philipp A. Witte and Ranveer Chandra and Russell J. Hewett and Felix J. Herrmann}
}
@presentation {herrmann2023ML4SEISMICmsc,
	title = {Monitoring subsurface CO2 plumes with learned sequential Bayesian inference},
	year = {2023},
	month = {11},
	abstract = {Reservoir engineers frequently employ two-phase flow simulations and history-matching to oversee and anticipate the behavior of CO2 plumes within geological carbon storage. These simulations, while valuable for gaining insights, face limitations due to several complex factors, such as uncertainties surrounding the plume{\textquoteright}s dynamics. To investigate this phenomenon more comprehensively, we introduce the concept of stochasticity in the dynamics, accounting for uncertainties in the underlying permeability of the reservoir. To enhance the accuracy of CO2 plume predictions and quantify the uncertainties involved, we utilize machine learning techniques to condition these predictions on time-lapse seismic and well observations. This framework works on the principle of sequential Bayesian inference that continuously assimilates information from time-lapse observations, updates the CO2 plume predictions, and characterizes uncertainties about the plumes.},
	keywords = {Bayesian inference, CCS, deep learning, Imaging, ML4SEISMIC, monitoring, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2023/herrmann2023ML4SEISMICmsc},
	author = {Abhinav Prakash Gahlot and Ting-ying Yu and Rafael Orozco and Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@conference {yu2023IMAGEmsc,
	title = {Monitoring Subsurface CO2 Plumes with Sequential Bayesian Inference},
	booktitle = {International Meeting for Applied Geoscience and Energy},
	year = {2023},
	note = {(IMAGE, Houston)},
	month = {08},
	abstract = {To monitor and predict CO2 plume dynamics during geological carbon storage, reservoir engineers usually perform two-phase flow simulations. While these simulations may provide useful insights, their usefulness is limited due to numerous complicating factors including uncertainty in the dynamics of the plume itself. To study this phenomenon, we consider stochasticity in the dynamic caused by unknown random changes in the injection rate. By conditioning the CO2 plume predictions on seismic observations, we correct the CO2 plume predictions and quantify uncertainty with machine learning.},
	keywords = {Bayesian inference, CCS, deep learning, Imaging, monitoring, SEG, Uncertainty quantification},
	url = {https://slimgroup.github.io/IMAGE2023/SequentialBayes/abstract.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2023/yu2023IMAGEmsc},
	author = {Ting-ying Yu and Abhinav Prakash Gahlot and Rafael Orozco and Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {herrmann2022ML4SEISMICmod,
	title = {Meet our digital twin for geological carbon storage},
	year = {2022},
	month = {11},
	abstract = {By embracing recent developments in simulation-based Bayesian inference{\textemdash}i.e., the task of deriving statistical information from a system based on in silico simulations{\textemdash}we envisage the development of an uncertainty-aware Digital Twin for seismic monitoring of Geologic Carbon Storage (GCS). According to IBM, {\textquotedblleft}A digital twin is a virtual representation of an object or system that spans its lifecycle, is updated from real-time data, and uses simulation, machine learning and reasoning to help decision-making{\textquotedblright}. This Digital Twin will be designed to maximally benefit from vastly improved abilities to simulate complex phenomena, including the development of CO2 plumes in saline aquifers, and from the ability of neural networks to learn by example as part of inference. For GCS, this means that systematic assessment of uncertainties now becomes possible when observing CO2 plumes from time-lapse geophysical data (e.g., seismic). Because the proposed Digital Twin{\textquoteright}s neural networks are taught to produce samples from the probability distribution for the CO2 plume conditioned by the observed time-lapse data, this approach will provide access to this information on uncertainty. As part of ML4Seismic, we are working on various aspects regarding the development of the Digital Twin including: (i) capability to generate realistic time-lapse data in response to CO2 injection in large strongly heterogeneous reservoirs. This simulation framework will facilitate the design of high-fidelity monitoring systems and is unique since it uses proxy Earth models with realistic CO2 plumes and heterogeneity; (ii) An inversion framework capable of producing high-fidelity time-lapse images of CO2 plumes and reservoir properties from time-lapse data collected in response to CO2 injection; (iii) uncertainty-aware data-assimilation framework based on techniques from sequential Bayes and capable of rapidly producing high-fidelity CO2 plume forecasts that are consistent with observed time-lapse data; (iv) A scalable uncertainty-aware early warning system designed to safeguard CO2 injection operations built on the latest insights from interpretable and trustworthy (explainable and robust) machine learning. After describing how to build a Digital Twin for GSC, early results will be presented on the use of Fourier Neural Networks as surrogates for the two-phase flow equations, seismic monitoring with our joint recovery model, and the use of spectral ratio to design low-cost acquisitions for time-lapse seismic.},
	keywords = {CCS, digital twin, GCS, ML4SEISMIC, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/herrmann2022ML4SEISMICmod/index.html},
	author = {Felix J. Herrmann}
}
@techreport {orozco2022MIDLmei,
	title = {Memory Efficient Invertible Neural Networks for 3D Photoacoustic Imaging},
	number = {TR-CSE-2022-2},
	year = {2022},
	month = {04},
	abstract = {Photoacoustic imaging (PAI) can image high-resolution structures of clinical interest such as vascularity in cancerous tumor monitoring. When imaging human subjects, geometric restrictions force limited-view data retrieval causing imaging artifacts. Iterative physical model based approaches reduce artifacts but require prohibitively time consuming PDE solves. Machine learning (ML) has accelerated PAI by combining physical models and learned networks. However, the depth and overall power of ML methods is limited by memory intensive training. We propose using invertible neural networks (INNs) to alleviate memory pressure. We demonstrate INNs can image 3D photoacoustic volumes in the setting of limited-view, noisy, and subsampled data. The frugal constant memory usage of INNs enables us to train an arbitrary depth of learned layers on a consumer GPU with 16GB RAM.},
	keywords = {invertible networks, medical imaging, photoacoustic imaging, Physics and Machine Learning Hybrid},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2022/orozco2022MIDLmei/midl_2022.html},
	author = {Rafael Orozco and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {louboutin2022ML4SEISMICmos,
	title = {ML4Seismic open-source software: updates and developments},
	year = {2022},
	month = {11},
	abstract = {Software is at the core of research and development in inverse problems. At SLIM, we have experience developing scalable and performant software, such as our legacy parallel MATLAB framework. With ML4Seismic, we are dedicated to build on this experience to develop HPC open source software (OSS) for the scientific community in collaboration with our partners. In this talk, we will describe our OSS Julia and Python environment, our high-level abstraction principles, and the range of solutions we offer for seismic processing and inversion and for machine learning. We will emphasize our aim to provide scalable software that can be easily applied to industrial problems.},
	keywords = {ML4SEISMIC, open-source, SLIM, software},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/louboutin2022ML4SEISMICmos/index.html},
	author = {Mathias Louboutin and Ziyi Yin and Rafael Orozco and Thomas J. Grady II and Felix J. Herrmann}
}
@presentation {yu2022ML4SEISMICmsb,
	title = {Monitoring with sequential Bayesian inference},
	year = {2022},
	month = {11},
	abstract = {For this study, we apply sequential Bayesian inference to monitor the time evolution of subsurface flow of CO2 from indirect acoustic measurements at the surface. Upon receiving new acoustic measurements, we infer the current state of the CO2 by sampling from a learned posterior. Using the incoming data, we then perform online updates of the current posterior. This is accomplished by using the fluid flow model to advance the estimated state variable forward in time in order to update the learned posterior. With a synthetic experiment, we demonstrate this method can track the flow evolution accurately as measured by PSNR metrics. Since the posterior is a learned network, we can compute estimates faster than traditional least squares methods. This method can also quantify the uncertainty due to stochasticity in fluid flow model and the limited-azimuth imaging configuration.},
	keywords = {CCS, conditional normalizing flows, GCS, ML4SEISMIC, monitoring, sequential Bayes, SLIM, time-lapse, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/yu2022ML4SEISMICmsb/index.html},
	author = {Ting-ying Yu and Rafael Orozco and Ziyi Yin 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 {zhang2017SEGmsd,
	title = {Massive 3D seismic data compression and inversion with hierarchical Tucker},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {1347-1352},
	abstract = {Modern-day oil and gas exploration, especially in areas of complex geology such as fault belts and sub-salt areas, is an increasingly expensive and risky endeavour. Typically long-offset and dense sampling seismic data are required for subsequent shot based processing procedures, e.g. wave-equation based inversion (WEI) and surface-related multiple elimination (SRME). However, these strict requirements result in an exponential growth in data volume size and prohibitive demands on computational resources, given the multidimensional nature of the data volumes. Moreover the physical constraints and cost limitations impose restrictions on acquiring fully sampled data. In this work, we propose to invert our large-scale data from a set of subsampled measurements, resulting in an estimate of the true volume in a compressed low-rank tensor format. Rather than expanding the data to its fully-sampled form for later downstream processes, we demonstrate how to use this compressed data directly via on-the-fly common shot or receiver gathers extraction. The combination of massive compression and fast on demand data reconstruction of 3D shot or receiver gathers leads to a substantial reduction in memory costs but with minimal effects on results in the subsequent processing procedures. We demonstrate the effective implementation of our proposed framework on full-waveform inversion on a 3D seismic synthetic data set generated from a Overthrust model.},
	keywords = {3D, FWI, SEG, tensor algebra},
	doi = {10.1190/segam2017-17742951.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/zhang2017SEGmsd/zhang2017SEGmsd.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/zhang2017SEGmsd/zhang2017SEGmsd_pres.pdf},
	author = {Yiming Zhang and Curt Da Silva and Rajiv Kumar and Felix J. Herrmann}
}
@presentation {zhang2017SINBADFmsd,
	title = {Massive seismic data compression \& recovery w/ on-the-fly data extraction},
	year = {2017},
	publisher = {SINBAD},
	abstract = {Industrial seismic exploration has moved towards complex geological areas, which requires typically long-offset and dense sampling data in order to avoid aliasing and inaccuracy in wave-equation based inversion algorithms. These strict requirements lead to massive data volume size and prohibitive demands on computational resources. In this work, we propose to compress our dense data in hierarchical Tucker tensor format by exploiting the low-rank structure of the data in a transformed domain. Then, we devise on-the-fly common shot or receiver gather extraction directly via the highly compressed factors. In subsampling scenarios, by interpolating this novel tensor format, we can also reconstruct the shot or receiver gather on a per-query basis rather than expanding the data to its fully-sampled form. We demonstrate the effective performance of our proposed technique on 3D stochastic full-waveform inversion, which allows the stochastic algorithm to extract shot gathers as it requires them throughout the inversion process. Moreover, we finally show how to computational effectively generate the CIGs from this compressed low-rank tensor representation of the data with the help of fast simultaneous shot or receiver gather generation.},
	keywords = {Presentation, SINBAD, SINBADFALL2017, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/zhang2017SINBADFmsd/zhang2017SINBADFmsd.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/zhang2017SINBADFmsd/zhang2017SINBADFmsd.mov},
	author = {Yiming Zhang and Curt Da Silva and Rajiv Kumar and Felix J. Herrmann}
}
@presentation {kumar2017SINBADFmdt,
	title = {Multi-domain target-oriented imaging using extreme-scale matrix factorization},
	year = {2017},
	publisher = {SINBAD},
	abstract = {In this work, we present an alternative approach to redatum both source and receivers at depth, under the framework of reflectivity-based extended images with two-way wave propagation in the background medium. We propose a randomized svd based probing scheme that takes advantage of the algebraic structure of the extended imaging system to overcome the computational cost and memory usage associated with the number of wave-equation solutions and explicit storage employed by conventional migration methods. Experimental results on complex geological models demonstrate the efficacy of proposed methodology in performing multi-domain target imaging.},
	keywords = {Presentation, SINBAD, SINBADFALL2017, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/kumar2017SINBADFmdt/kumar2017SINBADFmdt.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/kumar2017SINBADFmdt/kumar2017SINBADFmdt.mov},
	author = {Rajiv Kumar and Marie Graff-Kray and Ivan Vasconcelos and Felix J. Herrmann}
}
@article {li2015GEOPmgn,
	title = {Modified Gauss-Newton full-waveform inversion explained{\textendash}-why sparsity-promoting updates do matter},
	journal = {Geophysics},
	volume = {81},
	number = {3},
	year = {2016},
	note = {(Geophysics)},
	month = {05},
	pages = {R125-R138},
	abstract = {Full-waveform inversion can be formulated as a nonlinear least-squares optimization problem. This non-convex problem can be extremely computationally expensive because it requires repeatedly solving large linear systems that correspond to discretized partial differential equations. Randomized subsampling techniques allow us to work with small subsets of (monochromatic) source experiments, reducing the computational cost. However, this subsampling weakens subsurface illumination and introduces subsampling related incoherent artifacts. These subsampling-related artifacts{\textendash}-in conjunction with local minima that are known to plague full-waveform inversion{\textendash}-motivate us to come up with a technique to "regularize" this problem. Following earlier work, we take advantage of the fact that curvelets represent subsurface models and perturbations parsimoniously. At first impulse promoting sparsity on the model directly seems the most natural way to proceed, but we will demonstrate that in certain cases it can be advantageous to promote sparsity on the Gauss-Newton updates instead. While constraining the one-norm of the descent directions does not change not change the underlying full-waveform inversion objective, the constrained model updates remain descent directions, remove subsampling-related artifacts and improve the overall inversion result. We empirically observe this phenomenon in situations where the different model updates occur at roughly the same locations in the curvelet domain. We further investigate and analyze this phenomenon, where nonlinear inversions benefit from sparsity-promoting constraints on the updates, by means of a set of carefully selected examples including phase retrieval and full-waveform inversion. In all cases, we observe a faster decay of the residual and model error as a function of the number of iterations.},
	keywords = {Full-waveform inversion, Gauss-Newton method, sparsity promotion},
	doi = {10.1190/geo2015-0266.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2016/li2015GEOPmgn/li2015GEOPmgn.pdf},
	author = {Xiang Li and Ernie Esser and Felix J. Herrmann}
}
@conference {kumar2015EAGEmcu,
	title = {Matrix completion on unstructured grids : 2-D seismic data regularization and interpolation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2015},
	note = {(EAGE, Madrid)},
	month = {06},
	abstract = {Seismic data interpolation via rank-minimization techniques has been recently introduced in the seismic community. All the existing rank-minimization techniques assume the recording locations to be on a regular grid, e.g., sampled periodically, but seismic data are typically irregularly sampled along spatial axes. Other than the irregularity of the sampled grid, we often have missing data. In this paper, we study the effect of grid irregularity to conduct matrix completion on a regular grid for unstructured data. We propose an improvement of existing rank-minimization techniques to do regularization. We also demonstrate that we can perform seismic data regularization and interpolation simultaneously. We illustrate the advantages of the modification using a real seismic line from the Gulf of Suez to obtain high quality results for regularization and interpolation, a key application in exploration geophysics.},
	keywords = {EAGE, interpolation, matrix completion, NFFT, regularization},
	doi = {10.3997/2214-4609.201413448},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/kumar2015EAGEmcu/kumar2015EAGEmcu.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2015/kumar2015EAGEmcu/kumar2015EAGEmcu_poster.pdf},
	author = {Rajiv Kumar and Oscar Lopez and Ernie Esser and Felix J. Herrmann}
}
@conference {peters2015SIAMmfq,
	title = {Matrix-free quadratic-penalty methods for PDE-constrained optimization},
	booktitle = {SIAM Conference on Computational Science and Engineering},
	year = {2015},
	note = {(SIAM, Salt Lake City)},
	month = {03},
	abstract = {The large scale of seismic waveform inversion makes matrix free implementations essential. We show how to exploit the quadratic penalty structure to construct matrix free reduced-space and full-space algorithms, which have some advantages over the commonly used Lagrangian based methods for PDE-constrained optimization. This includes the construction of effective and sparse Hessian approximations and reduced sensitivity to the initial guess. A computational bottleneck is the need to solve a large least squares problem with a PDE block. When direct solvers are not available, we propose a fast matrix free iterative approach with reasonable memory requirements. It takes advantage of the structure of the least squares problem with a combination of preconditioning, low rank decomposition and deflation.},
	keywords = {least-squares, low-rank, PDE-constrained optimization, quadratic-penalty, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2015/peters2015SIAMmfq/peters2015SIAMmfq.pdf},
	author = {Bas Peters and Felix J. Herrmann and Chen Greif}
}
@techreport {kumar2014SEGmcu,
	title = {Matrix completion on unstructured grids : 2-D seismic data regularization and interpolation},
	number = {TR-EOAS-2014-3},
	year = {2014},
	month = {04},
	institution = {UBC},
	abstract = {Seismic data interpolation via rank-minimization techniques has been recently introduced in the seismic community. All the existing rank-minimization techniques assume the recording locations to be on a regular grid, e.g. sampled periodically, but seismic data are typically irregularly sampled along spatial axes. Other than the irregularity of the sampled grid, we often have missing data. In this paper, we study the effect of grid irregularity to conduct matrix completion on a regular grid for unstructured data. We propose an improvement of existing rank-minimization techniques to do regularization. We also demonstrate that we can perform seismic data regularization and interpolation simultaneously. We illustrate the advantages of the modification using a real seismic line from the Gulf of Suez to obtain high quality results for regularization and interpolation, a key application in exploration geophysics.},
	keywords = {interpolation, matrix completion, NFFT, regularization},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/kumar2014SEGmcu/kumar2014SEGmcu.html},
	author = {Rajiv Kumar and Oscar Lopez and Ernie Esser and Felix J. Herrmann}
}
@presentation {lago2014SINBADmri,
	title = {Minimal-residual iterative methods for time-harmonic wave-equation},
	year = {2014},
	publisher = {SINBAD},
	abstract = {In this work we aim at comparing the performance of some iterative methods for solving the time-harmonic acoustic wave-equation, one of the most challenging problems in the numerical linear algebra community. Widely used in frequency domain full waveform inversion, the discrete wave-equation yields very large, complex, sparse, ill-conditioned linear systems. In this extended abstract we aim at further comparing our recently proposed method, CRMN, against CGMN and another method renown for being very memory efficient, the two-level preconditioner with shifted Laplacian operator. We propose several improvements for the two-level preconditioner by combining this method with CRMN in several senses.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/lago2014SINBADmri/lago2014SINBADmri.pdf},
	author = {Rafael Lago and Felix J. Herrmann}
}
@conference {lin2014SEGmdg,
	title = {Mitigating data gaps in the estimation of primaries by sparse inversion without data reconstruction},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2014},
	note = {(SEG)},
	month = {10},
	pages = {4157-4161},
	abstract = {We propose to solve the Estimation of Primaries by Sparse Inversion problem from a sesimic record with missing near-offsets and large holes without any explicit data reconstruction, by instead simulating the missing multiple contributions with terms involving auto-convolutions of the primary wavefield. Exclusion of the unknown data as an inversion variable from the REPSI process is desireable, since it eliminates a significant source of local minima that arises from attempting to invert for the unobserved traces using primary and multiple models that may be far-away from the true solution. In this talk we investigate the necessary modifications to the Robust EPSI algorithm to account for the resulting non-linear modeling operator, and demonstrate that just a few auto-convolution terms are enough to satisfactorily mitigate the effects of data gaps during the inversion process.},
	keywords = {algorithm, EPSI, inversion, multiples, REPSI, SEG},
	doi = {http://dx.doi.org/10.1190/segam2014-1680.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/lin2014SEGmdg/lin2014SEGmdg.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/lin2014SEGmdg/lin2014SEGmdg_pres.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {lin2014SINBADmas,
	title = {Multilevel acceleration strategy for REPSI},
	year = {2014},
	publisher = {SINBAD},
	abstract = {This talk discusses a multilevel inversion strategy that aims to substantially reduce the computational costs of the Robust Estimation of Primaries by Sparse Inversion algorithm. The proposed method solves early iterations of REPSI at very coarse spatial sampling grids while gradually ramping-up the spatial sampling when more accuracy is desired. No changes to the the core implementation of the original algorithm are necessary while in addition only requiring trace decimation, low-pass filtering, and rudimentary interpolation techniques.},
	keywords = {Presentation, SINBAD, SINBADSPRING2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Spring/lin2014SINBADmas/lin2014SINBADmas.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {lin2014EAGEmas,
	title = {Multilevel acceleration strategy for the robust estimation of primaries by sparse inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {We propose a method to substantially reduce the computational costs of the Robust Estimation of Primaries by Sparse Inversion algorithm, based on a multilevel inversion strategy that shifts early iterations of the method to successively coarser spatial sampling grids. This method requires no change in the core implementation of the original algorithm, and additionally only relies on trace decimation, low-pass filtering, and rudimentary interpolation techniques. We furthermore demonstrate with a synthetic seismic line significant computational speedups using this approach.},
	keywords = {EAGE, EPSI, multigrid, multilevel, multiples, multiscale, REPSI},
	doi = {10.3997/2214-4609.20140672},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/lin2014EAGEmas/lin2014EAGEmas.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/lin2014EAGEmas/lin2014EAGEmas_pres.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {peters2014SINBADmpw,
	title = {Multi-parameter waveform inversion; exploiting the structure of penalty-methods},
	year = {2014},
	publisher = {SINBAD},
	abstract = {In this talk I consider the problem of inverting waveforms for multiple medium parameters. The governing PDE is chosen to be the Helmholtz equation with compressibility and buoyancy as the unknowns. Both unknowns occur in the same equation and practice has shown it is very hard to estimate both equally accurate; the buoyancy estimate (or density if a slightly different parametrization is used) is typically much smoother than the compressibility (or velocity). Here I introduce a new waveform inversion algorithm: a full Newton-type method based on a penalty method which adds the PDE constraint as a quadratic penalty term. This method updates both the {\textquoteright}wavefields{\textquoteright} and medium parameters, without explicitly solving PDE{\textquoteright}s. One of the main advantages is the availability of a sparse Hessian and exact gradient which are not the result of any PDE solves. We asses if the availability of the Hessian, which includes information about the coupling between the two medium parameters, can help reconstruct both compressibility and buoyancy.},
	keywords = {Presentation, SINBAD, SINBADSPRING2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Spring/peters2014SINBADmpw/peters2014SINBADmpw.pdf},
	author = {Bas Peters and Felix J. Herrmann}
}
@presentation {akalin2013SINBADmtc,
	title = {Matrix and tensor completion for large-scale seismic interpolation: a comparative study},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Owing to their high dimensionality, interpolating 3D seismic data volumes remains a computationally daunting task. In this work, we outline a comprehensive framework for sampling and interpolating such volumes based on the well-understood theory of Matrix and Tensor completion. This interpolation theory consists of three components major signal structure, structure-destroying sampling, and structure-restoring optimization. By viewing interpolation in the context of this theory, we are able to specify exactly when these approaches are expected to perform well. We also introduce structure-revealing transformations that promote the inherent low-rank structure in seismic data as well as a factorization approach that scales to large problem sizes. Our methods are able to handle large-scale data volumes more accurately and more quickly compared to other more ad-hoc approaches, as we will demonstrate. This is joint work with Curt Da Silva, Rajiv Kumar, Ben Recht, and Felix J. Herrmann.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/akalin2013SINBADmtc/akalin2013SINBADmtc.pdf},
	author = {Okan Akalin and Curt Da Silva and Rajiv Kumar and Ben Recht and Felix J. Herrmann}
}
@article {vanLeeuwen2013GJImlm,
	title = {Mitigating local minima in full-waveform inversion by expanding the search space},
	journal = {Geophysical Journal International},
	volume = {195},
	year = {2013},
	month = {10},
	pages = {661-667},
	abstract = {Wave equation based inversions, such as full-waveform inversion and reverse-time migration, are challenging because of their computational costs, memory requirements and reliance on accurate initial models. To confront these issues, we propose a novel formulation of wave equation based inversion based on a penalty method. In this formulation, the objective function consists of a data-misfit term and a penalty term, which measures how accurately the wavefields satisfy the wave equation. This new approach is a major departure from current formulations where forward and adjoint wavefields, which both satisfy the wave equation, are correlated to compute updates for the unknown model parameters. Instead, we carry out the inversions over two alternating steps during which we first estimate the wavefield everywhere, given the current model parameters, source and observed data, followed by a second step during which we update the model parameters, given the estimate for the wavefield everywhere and the source. Because the inversion involves both the synthetic wavefields and the medium parameters, its search space is enlarged so that it suffers less from local minima. Compared to other formulations that extend the search space of wave equation based inversion, our method differs in several aspects, namely (i) it avoids storage and updates of the synthetic wavefields because we calculate these explicitly by finding solutions that obey the wave equation and fit the observed data and (ii) no adjoint wavefields are required to update the model, instead our updates are calculated from these solutions directly, which leads to significant computational savings. We demonstrate the validity of our approach by carefully selected examples and discuss possible extensions and future research.},
	doi = {10.1093/gji/ggt258},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalJournalInternational/2013/vanLeeuwen2013GJImlm/vanLeeuwen2013mlm.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@presentation {herrmann2013SINBADmlm,
	title = {Mitigating local minima in full-waveform inversion by expanding the search space with the penalty method},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Wave-equation based inversions, such as full-waveform inversion, are challenging because of their computational costs, memory requirements, and reliance on accurate initial models. To confront these issues, we propose a novel formulation of full-waveform inversion based on a penalty method. In this formulation, the objective function consists of a data-misfit term and a penalty term which measures how accurately the wavefields satisfy the wave-equation. Because we carry out the inversion over a larger search space, including both the model and synthetic wavefields, our approach suffers less from local minima. Our main contribution is the development of an efficient optimization scheme that avoids having to store and update the wavefields by explicit elimination. Compared to existing optimization strategies for full-waveform inversion, our method differers in two main aspects; i. The wavefields are solved from an augmented wave-equation, where the solution is forced to solve the wave-equation and fit the observed data, ii. no adjoint wavefields are required to update the model, which leads to significant computational savings. We demonstrate the validity of our approach by carefully selected examples and discuss possible extensions and future research. This is joint work with Tristan van Leeuwen.},
	keywords = {Presentation, SINBAD, SINBADSPRING2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Spring/herrmann2013SINBADmlm/herrmann2013SINBADmlm.pdf},
	author = {Felix J. Herrmann}
}
@presentation {li2013SINBADmsd,
	title = {Model-space versus data-space FWI with the acoustic wave equation},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Inverting data with elastic phases using an acoustic wave equation can lead to erroneous results, especially when the number of iterations is too high, which may lead to over fitting the data. Several approaches have been proposed to address this issue. Most commonly, people data- filtering operations that are aimed to deemphasize the elastic phases in the data in favor of the acoustic phases. Examples of this approach are nested loops over offset range and Laplace parameters. In this presentation, we discuss two complementary optimization-driven methods where the minimization process decides adaptively which of the data or model components are consistent with the objective. Specifically, we compare the s t misfit function as the data-space alternative and curvelet-domain sparsity promotion as the model-space alternative. Application of these two methods to a realistic synthetic lead to comparable results that we believe can be improved by combining these two methods.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/li2013SINBADmsd/li2013SINBADmsd.pdf},
	author = {Xiang Li and Anais Tamalet and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {dasilva2012EAGEprobingprecond,
	title = {Matrix probing and simultaneous sources: a new approach for preconditioning the Hessian},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2012},
	month = {06},
	abstract = {Recent advances based on the mathematical understanding of the Hessian as, under certain conditions, a pseudo-differential operator have resulted in a new preconditioner by L. Demanet et al. Basing their approach on a suitable basis expansion for the Hessian, by suitably {\textquoteright}probing{\textquoteright} the Hessian, i.e. applying the Hessian to a small number of randomized model perturbations, one can obtain an approximation to the inverse Hessian in an efficient manner. Building upon this approach, we consider this preconditioner in the context of least-squares migration and Full Waveform Inversion and specifically dimensionality reduction techniques in these domains. By utilizing previous work in simultaneous sources, we are able to develop an efficient least-squares migration scheme which recovers higher quality images and hence higher quality search directions in the context of a Gauss-Newton method for Full Waveform Inversion while simultaneously avoiding inordinate amounts of additional work.},
	keywords = {EAGE, matrix probing, pseudo-differential operator},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/dasilva2012EAGEprobingprecond/dasilva2012EAGEprobingprecond.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/dasilva2012EAGEprobingprecond/dasilva2012EAGEprobingprecond_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=59193},
	author = {Curt Da Silva and Felix J. Herrmann}
}
@conference {tu2011SEGmult,
	title = {Migration with surface-related multiples from incomplete seismic data},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {30},
	year = {2011},
	month = {09},
	pages = {3222-3227},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Seismic acquisition is confined by limited aperture that leads to finite illumination, which, together with other factors, hinders imaging of subsurface objects in complex geological settings such as salt structures. Conventional processing, including surface-related multiple elimination, further reduces the amount of information we can get from seismic data. With the growing consensus that multiples carry valuable information that is missing from primaries, we are motivated to exploit the extra illumination provided by multiples to image the sub- surface. In earlier research, we proposed such a method by combining primary estimation and sparsity-promoting migration to invert for model perturbations directly from the total up-going wavefield. In this abstract, we focus on a particular case. By exploiting the extra illumination from surface-related multiples, we mitigate the effects caused by migrating from incomplete data with missing sources and missing near-offsets.},
	keywords = {Imaging, Presentation, Processing, SEG},
	doi = {10.1190/1.3627865},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/tu11SEGmult/tu11SEGmult.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/tu11SEGmult/tu11SEGmult_pres.pdf},
	author = {Ning Tu and Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {li2011SBGFmgnsu,
	title = {Modified Gauss-Newton with sparse updates},
	booktitle = {SBGF},
	year = {2011},
	publisher = {SBGF},
	organization = {SBGF},
	abstract = {Full-waveform inversion (FWI) is a data fitting procedure that relies on the collection of seismic data volumes and sophisticated computing to create high-resolution models.With the advent of FWI, the improvements in acquisition and inversion have been substantial, but these improvements come at a high cost because FWI involves extremely large multi-experiment data volumes. The main obstacle is the {\textquoteleft}curse of dimensionality{\textquoteright} exemplified by Nyquist{\textquoteright}s sampling criterion, which puts a disproportionate strain on current acquisition and processing systems as the size and desired resolution increases. In this paper, we address the {\textquoteleft}curse of dimensionality{\textquoteright} by using randomized dimensionality reduction of the FWI problem, coupled with a modified Gauss-Newton (GN) method designed to promote curvelet-domain sparsity of model updates. We solve for these updates using the spectral projected gradient method, implemented in the SPG1 software package. Our approach is successful because it reduces the size of seismic data volumes without loss of information. With this reduction, we can compute Gauss-Newton updates with the reduced data volume at the cost of roughly one gradient update for the fully sampled wavefield},
	keywords = {Full-waveform inversion, SBGF},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SBGF/2011/li11SBGFmgnsu/li11SBGFmgnsu.pdf},
	author = {Xiang Li and Felix J. Herrmann and Tristan van Leeuwen and Aleksandr Y. Aravkin}
}
@conference {herrmann2011SPIEmsp,
	title = {A modified, sparsity promoting, Gauss-Newton algorithm for seismic waveform inversion},
	booktitle = {Proc. SPIE},
	number = {81380V},
	year = {2011},
	month = {08},
	abstract = {Images obtained from seismic data are used by the oil and gas industry for geophysical exploration. Cutting-edge methods for transforming the data into interpretable images are moving away from linear approximations and high-frequency asymptotics towards Full Waveform Inversion (FWI), a nonlinear data-fitting procedure based on full data modeling using the wave-equation. The size of the problem, the nonlinearity of the forward model, and ill-posedness of the formulation all contribute to a pressing need for fast algorithms and novel regularization techniques to speed up and improve inversion results. In this paper, we design a modified Gauss-Newton algorithm to solve the PDE- constrained optimization problem using ideas from stochastic optimization and compressive sensing. More specifically, we replace the Gauss-Newton subproblems by randomly subsampled, -$\ell_1$ regularized subproblems. This allows us us significantly reduce the computational cost of calculating the updates and exploit the compressibility of wavefields in Curvelets. We explain the relationships and connections between the new method and stochastic optimization and compressive sensing (CS), and demonstrate the efficacy of the new method on a large-scale synthetic seismic example.},
	keywords = {Compressive Sensing, Full-waveform inversion, Optimization, SLIM},
	issn = {1},
	doi = {10.1117/12.893861},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SPIE/2011/herrmann2011SPIEmsp/herrmann2011SPIEmsp.pdf},
	author = {Felix J. Herrmann and Xiang Li and Aleksandr Y. Aravkin and Tristan van Leeuwen}
}
@conference {erlangga2009EAGEmwi,
	title = {Migration with implicit solvers for the time-harmonic Helmholtz equation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2009},
	month = {06},
	abstract = {From the measured seismic data, the location and the amplitude of reflectors can be determined via a migration algorithm. Classically, following Claerbout{\textquoteright}s imaging principle [2], a reflector is located at the position where the source{\textquoteright}s forward-propagated wavefield correlates with the backward-propagated wavefield of the receiver data. Lailly and Tarantola later showed that this imaging principle is an instance of inverse problems, with the associated migration operator formulated via a least-squares functional; see [6, 12, 13]. Furthermore, they showed that the migrated image is associated with the gradient of this functional with respect to the image. If the solution of the least-squares functional is done iteratively, the correlation-based image coincides up to a constant with the first iteration of a gradient method. In practice, this migration is done either in the time domain or in the frequency domain. In the frequency-domain migration, the main bottleneck thus far, which renders its full implementation to large scale problems, is the lack of efficient solvers for computing wavefields. Robust direct methods easily run into excessive memory requirements as the size of the problem increases. On the other hand, iterative methods, which are less demanding in terms of memory, suffered from lack of convergence. During the past years, however, progress has been made in the development of an efficient iterative method [4, 3] for the frequency-domain wavefield computations. In this paper, we will show the significance of this method (called MKMG) in the context of the frequency-domain migration, where multi-shot-frequency wavefields (of order of 10,000 related wavefields) need to be computed.},
	keywords = {EAGE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2009/Erlangga09EAGEmwi/Erlangga09EAGEmwi.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2009/Erlangga09EAGEmwi/Erlangga09EAGEmwi_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=23955},
	author = {Yogi A. Erlangga and Felix J. Herrmann}
}
@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 {herrmann2007SEGmpf,
	title = {Multiple prediction from incomplete data with the focused curvelet transform},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {26},
	year = {2007},
	pages = {2505-2600},
	abstract = {Incomplete data represents a major challenge for a successful prediction and subsequent removal of multiples. In this paper, a new method will be represented that tackles this challenge in a two-step approach. During the first step, the recenly developed curvelet-based recovery by sparsity-promoting inversion (CRSI) is applied to the data, followed by a prediction of the primaries. During the second high-resolution step, the estimated primaries are used to improve the frequency content of the recovered data by combining the focal transform, defined in terms of the estimated primaries, with the curvelet transform. This focused curvelet transform leads to an improved recovery, which can subsequently be used as input for a second stage of multiple prediction and primary-multiple separation.},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2792987},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/herrmann07SEGmpf/herrmann07SEGmpf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/herrmann07SEGmpf/herrmann07SEGmpf_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {verschuur2007SEGmmp,
	title = {Multiterm multiple prediction using separated reflections and diffractions combined with curvelet-based subtraction},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {26},
	year = {2007},
	pages = {2535-2539},
	publisher = {SEG},
	organization = {SEG},
	abstract = {The surface-related multiple elimination (SRME) method has proven to be successful on a large number of data cases. Most of the applications are still 2D, as the full 3D implementation is still expensive and under development. However, the earth is a 3D medium, such that 3D effects are difficult to avoid. Most of the 3D effects come from diffractive structures, whereas the specular reflections normally have less of a 3D behavior. By separating the seismic data in a specular reflecting and a diffractive part, multiple prediction can be carried out with these different subsets of the input data, resulting in several categories of predicted multiples. Because each category of predicted multiples can be subtracted from the input data with different adaptation filters, a more flexible SRME procedure is obtained. Based on some initial results from a Gulf of Mexico dataset, the potential of this approach is investigated. \copyright2007 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.2792993},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/verschuur07SEGmmp/verschuur07SEGmmp.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2007/verschuur07SEGmmp/verschuur07SEGmmp_pres.pdf},
	author = {D. J. Verschuur and Deli Wang and Felix J. Herrmann}
}
@conference {herrmann2006SINBADmpf,
	title = {Multiple prediction from incomplete data},
	booktitle = {SINBAD 2006},
	year = {2006},
	keywords = {Presentation, SINBAD, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/herrmann2006SINBADmpf/herrmann2006SINBADmpf.pdf},
	author = {Felix J. Herrmann}
}
@conference {moghaddam2004SEGmpw,
	title = {Migration preconditioning with curvelets},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {23},
	year = {2004},
	pages = {2204-2207},
	publisher = {SEG},
	organization = {SEG},
	abstract = {In this paper, the property of Curvelet transforms for preconditioning the migration and normal operators is investigated. These operators belong to the class of Fourier integral operators and pseudo-differential operator, respectively. The effect of this pre-conditioner is shown in term of improvement of sparsity, convergence rate, number of iteration for the Krylov-subspace solver and clustering of singular(eigen) values. The migration operator, which we employed in this work is the common-offset Kirchoff-Born migration. \copyright2004 Society of Exploration Geophysicists},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.1845213},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2004/Moghaddam04SEGmpw/Moghaddam04SEGmpw_paper.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2004/Moghaddam04SEGmpw/Moghaddam04SEGmpw_pres.pdf},
	author = {Peyman P. Moghaddam and Felix J. Herrmann}
}
@conference {herrmann2003SPIEmsa,
	title = {Multifractional splines: application to seismic imaging},
	booktitle = {Proceedings of SPIE Technical Conference on Wavelets: Applications in Signal and Image Processing X},
	volume = {5207},
	year = {2003},
	pages = {240-258},
	publisher = {SPIE},
	organization = {SPIE},
	abstract = {Seismic imaging commits itself to locating singularities in the elastic properties of the Earth{\textquoteright}s subsurface. Using the high-frequency ray-Born approximation for scattering from non-intersecting smooth interfaces, seismic data can be represented by a generalized Radon transform mapping the singularities in the medium to seismic data. Even though seismic data are bandwidth limited, signatures of the singularities in the medium carry through this transform and its inverse and this mapping property presents us with the possibility to develop new imaging techniques that preserve and characterize the singularities from incomplete, bandwidth-limited and noisy data. In this paper we propose a non-adaptive Curvelet/Contourlet technique to image and preserve the singularities and a data-adaptive Matching Pursuit method to characterize these imaged singularities by Multi-fractional Splines. This first technique borrows from the ideas within the Wavelet-Vaguelette/Quasi-SVD approach. We use the almost diagonalization of the scattering operator to approximately compensate for (i) the coloring of the noise and hence facilitate estimation; (ii) the normal operator itself. Results of applying these techniques to seismic imaging are encouraging although many open fundamental questions remain.},
	keywords = {Presentation, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SPIE/2003/herrmann2003SPIEmsa/herrmann2003SPIEmsa.pdf},
	author = {Felix J. Herrmann},
	editor = {Michael A. Unser and Akram Aldroubi and Andrew F. Laine}
}
