@conference {orozco2025SIAMisu,
	title = {Industry-Scale Uncertainty-Aware Full Waveform Inference with Generative Models},
	booktitle = {SIAM Conference on Computational Science and Engineering (CSE25)},
	year = {2025},
	note = {(SIAM CSE25, Dallas)},
	month = {03},
	abstract = {In this talk, we address the challenge of Bayesian sampling for ill-posed inverse problems involving expensive PDE forward operators. To tackle this, we propose the use of generative models and discuss three key challenges along with our solutions. First, we address the constraints of GPU memory by introducing patch-based training and memory-efficient invertible networks, enabling the handling of large-scale data. Second, we demonstrate that these models can be effectively trained using only prior data available from acoustic observations and borehole well data, making the approach practical for real-world applications. Third, we explore various strategies to enhance the reliability of posterior samples by incorporating physics-based constraints through the wave operator. We conclude by presenting experiments that showcase the capabilities of these methods in field-data Full Waveform Inversion (FWI) workflows, scaling up to industry-scale problems with large 2D (512x7000 degrees of freedom) and 3D models.},
	keywords = {Bayesian sampling, FWI, Generative models, Inverse problems, Normalizing flows, SIAM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAMCSE/2025/orozco2025SIAMisu},
	author = {Rafael Orozco and Huseyin Tuna Erdinc and Mathias Louboutin and Felix J. Herrmann}
}
@conference {gahlot2025SIAMiac,
	title = {It{\textquoteright}s All in the Context: Sensitivity-Aware Digital Twins for Underground Storage},
	booktitle = {SIAM Conference on Mathematical \& Computational Issues in the Geosciences, Baton Rouge},
	year = {2025},
	month = {10},
	keywords = {Amortized Variational Inference, Bayesian inference, conditional normalizing flows, data assimilation, decision making, digital twin, experimental design, GCS, Imaging, Inverse problems, permeability, reservoir simulation, rock physics, RTM, SIAM, Summary Statistics, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2025/gahlot2025SIAMiac},
	author = {Abhinav Prakash Gahlot and Ipsita Bhar and Felix J. Herrmann}
}
@presentation {zeng2024ML4SEISMICiic,
	title = {Image Impeccable Challenge: An Effective Machine Learning Denoising Method for 3D Seismic Volumes},
	year = {2024},
	month = {11},
	abstract = {Seismic denoising is essential for enhancing the clarity, accuracy, and reliability of seismic data. Traditional seismic denoising methods, while effective for specific types of noise, often rely on well-established mathematical techniques that can be time-consuming, require manual tuning, and struggle with more complex noise patterns. Leveraging the 500 paired synthetic seismic datasets provided by the Think Onward community, we incorporate a 3D U-Net deep learning model with residual blocks and spatial attention to capture both local and global features for the seismic denoising task. During training, we apply the Laplacian operator to preserve edge details, followed by the Structural Similarity Index Measure (SSIM) loss to fine-tune the model, effectively removing concurrent noise and recovering the original seismic information. The resulting individual model achieves an SSIM of 0.99 compared to the ground truth seismic data. Additionally, we implement Langevin dynamics and Equivariant Bootstrapping techniques to estimate uncertainty during the training and inference phases, further improving the robustness of the denoising process.},
	keywords = {CAM, CCS, classification, explainability, GCS, Imaging, Inverse problems, JRM, ML4SEISMIC, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2024/zeng2024ML4SEISMICiic},
	author = {Shiqin Zeng and Rafael Orozco and Huseyin Tuna Erdinc 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 {erdinc2023ML4SEISMICias,
	title = {Improved automatic seismic CO2 leakage detection via dataset augmentation},
	year = {2023},
	month = {11},
	abstract = {Previous works showed that neural classifiers can be trained to detect CO2 leakage from time-lapse seismic images. While this result is crucial to the global deployment of geological carbon storage (GCS), its success depends on relatively dense non-replicated time-lapse data acquisition. In this study, we present an approach to enhance the detection accuracy and robustness of CO2 leakage detection by augmenting the training dataset with a variety of coarsely sampled receiver data and their corresponding receiver numbers. This augmentation strategy is particularly beneficial for scenarios where low-cost coarse receiver samplings, such as with ocean bottom nodes (OBNs), are utilized. Furthermore, we explore interpretability of the classifier{\textquoteright}s decisions by generating saliency maps for further analysis.},
	keywords = {CCS, classifier, deep learning, leakage detection, ML4SEISMIC, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2023/erdinc2023ML4SEISMICias},
	author = {Huseyin Tuna Erdinc and Abhinav Prakash Gahlot and Mathias Louboutin and Felix J. Herrmann}
}
@conference {gahlot2023NIPSWSifp,
	title = {Inference of CO2 flow patterns {\textendash} a feasibility study},
	booktitle = {Neural Information Processing Systems (NeurIPS)},
	year = {2023},
	note = {(NeurIPS 2023 Workshop - Tackling Climate Change with Machine Learning (Spotlight))},
	month = {10},
	abstract = {As the global deployment of carbon capture and sequestration (CCS) technology intensifies in the fight against climate change, it becomes increasingly imperative to establish robust monitoring and detection mechanisms for potential underground CO$_2$ leakage, particularly through pre-existing or induced faults in the storage reservoir{\textquoteright}s seals. While techniques such as history matching and time-lapse seismic monitoring of CO$_2$ storage have been used successfully in tracking the evolution of CO$_2$ plumes in the subsurface, these methods lack principled approaches to characterize uncertainties related to the CO$_2$ plumes{\textquoteright} behavior. Inclusion of systematic assessment of uncertainties is essential for risk mitigation for the following reasons: (i) CO$_2$ plume-induced changes are small and seismic data is noisy; (ii) changes between regular and irregular (e.g., caused by leakage) flow patterns are small; and (iii) the reservoir properties that control the flow are strongly heterogeneous and typically only available as distributions. To arrive at a formulation capable of inferring flow patterns for regular and irregular flow from well and seismic data, the performance of conditional normalizing flow will be analyzed on a series of carefully designed numerical experiments. While the inferences presented are preliminary in the context of an early CO$_2$ leakage detection system, the results do indicate that inferences with conditional normalizing flows can produce high-fidelity estimates for CO$_2$ plumes with or without leakage. We are also confident that the inferred uncertainty is reasonable because it correlates well with the observed errors. This uncertainty stems from noise in the seismic data and from the lack of precise knowledge of the reservoir{\textquoteright}s fluid flow properties.},
	keywords = {Amortized Variational Inference, Bayesian inference, CCS, conditional normalizing flows, geological carbon storage, monitoring, NIPS, Summary Statistics},
	doi = {10.48550/arXiv.2311.00290},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2023/gahlot2023NIPSWSifp/paper.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/NIPS/2023/gahlot2023NIPSWSifp/poster.pdf},
	author = {Abhinav Prakash Gahlot and Huseyin Tuna Erdinc and Rafael Orozco and Ziyi Yin and Felix J. Herrmann}
}
@presentation {yin2023CSEslim,
	title = {Introduction to Seismic Laboratory for Imaging and Modeling},
	year = {2023},
	note = {(CSE Student Recruiting Event)},
	month = {11},
	abstract = {We introduce the latest research developments in Seismic Laboratory for Imaging and Modeling (SLIM), including geological carbon storage monitoring, seismic and medical imaging and uncertainty quantification, and advancements in scientific machine learning and high performance computing.},
	keywords = {CCS, deep learning, Fourier neural operators, GCS, Inverse problems, learned constraints, learned surrogates, medical imaging, multiphysics, Normalizing flows, PDE, SLIM, Uncertainty quantification},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/CSE/2023/SLIM.pdf},
	author = {Ziyi Yin}
}
@presentation {herrmann2022ML4SEISMICintro,
	title = {Introduction to 2022 ML4SEISMIC Partners Meeting},
	year = {2022},
	month = {11},
	keywords = {ML4SEISMIC, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2022/herrmann2022ML4SEISMICintro/index.html},
	author = {Felix J. Herrmann}
}
@presentation {yin2021ML4SEISMICism,
	title = {Improved seismic monitoring of CO2 sequestration with the weighted joint recovery model},
	year = {2021},
	month = {11},
	abstract = {Time-lapse seismic monitoring of CO2 sequestration is challenging because the time-lapse signature of CO2 plumes is weak in amplitude and often contaminated by imaging artifacts due to coarsely sampled, noisy, and non-replicated surveys. In this talk, we present a sparsity-promoting least-squares imaging method where the baseline, and the current and past monitor surveys are inverted jointly. We demonstrate that the sensitivity of seismic monitoring can be improved by inverting for the common component{\textemdash}i.e., the component shared by all vintages, and innovations with respect to this common component. Combining this joint approach with weighted l1,2-norm minimization leads to a monitoring scheme capable of detecting irregular CO2-plume growth in a realistic geological setting.},
	keywords = {CCS, Compressive Sensing, Imaging, JRM, ML4SEISMIC, SLIM, time-lapse},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/yin2021ML4SEISMICism/Tue-11-20-Yin.html},
	author = {Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {zhang2021ML4SEISMICiss,
	title = {Improved seismic survey design by maximizing the spectral gap with global optimization},
	year = {2021},
	month = {11},
	abstract = {Random subsampling is increasingly being used in the acquisition of seismic data to shorten the acquisition time and to reduce costs. However, the design of optimal acquisition geometries is still an ongoing area of research. Matrix completion (MC) is a computationally efficient method to reconstruct fully sampled wavefields from sparsely sampled seismic data. In MC theory, the spectral gap (SG), which is a measure of the connectedness of the graph in expander graph theory, has been used to predict, and to some degree quantify, the quality of wavefield reconstruction, given a specific subsampling scheme (acquisition mask). Building on these insights, we propose an optimization scheme, based on simulated annealing, which finds subsampling masks with large SGs that improve the quality of wavefield reconstruction with MC. The experimental results show that the proposed method successfully increases the SG of the subsampling mask starting from randomly initialized masks. Increasing the SG leads to improved connectivity between the sources and receivers and therefore of the wavefield reconstruction. Numerical experiments confirm a direct relationship between increased SG and improved reconstruction quality. This confirms the value SG analysis brings to the design of seismic surveys without the need to carry out expensive wavefield reconstructions to optimize the acquisition design.},
	keywords = {Acquisition, Compressive Sensing, ML4SEISMIC, SLIM, survey design, wavefield reconstruction},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/zhang2021ML4SEISMICiss/Tue-10-30-Zhang.pdf},
	author = {Yijun Zhang and Felix J. Herrmann}
}
@presentation {herrmann2021ML4SEISMICintro,
	title = {Introduction inaugural ML4Seismic Partners Meeting},
	year = {2021},
	month = {11},
	abstract = {During this presentation, an overview of the 2021 ML4Seismic Program will be given including organization of the meeting, setup of ML4Seismic, and the Informal Sessions in the afternoon.},
	keywords = {ML4SEISMIC, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/herrmann2021ML4SEISMICintro/Mon-09-00-Herrmann.pdf},
	author = {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}
}
@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}
}
@mastersthesis {peters2019THiso,
	title = {Intersections and sums of sets for the regularization of inverse problems},
	year = {2019},
	note = {(PhD)},
	month = {05},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {Inverse problems in the imaging sciences encompass a variety of applications. The primary problem of interest is the identification of physical parameters from observed data that come from experiments governed by partial-differential-equations. The secondary type of imaging problems attempts to reconstruct images and video that are corrupted by, for example, noise, subsampling, blur, or saturation. The quality of the solution of an inverse problem is sensitive to issues such as noise and missing entries in the data. The non-convex seismic full-waveform inversion problem suffers from parasitic local minima that lead to wrong solutions that may look realistic even for noiseless data. To meet some of these challenges, I propose solution strategies that constrain the model parameters at every iteration to help guide the inversion. To arrive at this goal, I present new practical workflows, algorithms, and software, that avoid manual tuning-parameters and that allow us to incorporate multiple pieces of prior knowledge. Opposed to penalty methods, I avoid balancing the influence of multiple pieces of prior knowledge by working with intersections of constraint sets. I explore and present advantages of constraints for imaging. Because the resulting problems are often non-trivial to solve, especially on large 3D grids, I introduce faster algorithms, dedicated to computing projections onto intersections of multiple sets. To connect prior knowledge more directly to problem formulations, I also combine ideas from additive models, such as cartoon-texture decomposition and robust principal component analysis, with intersections of multiple constraint sets for the regularization of inverse problems. The result is an extension of the concept of a Minkowski set. Examples from non-unique physical parameter estimation problems show that constraints in combination with projection methods provide control over the model properties at every iteration. This can lead to improved results when the constraints are carefully relaxed.},
	keywords = {FWI, Optimization, PhD, regularization, Sets},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2019/peters2019THiso/peters2019THiso.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2019/peters2019THiso/peters2019THiso_pres.pdf},
	author = {Bas Peters}
}
@conference {peters2018CMSWMissrip,
	title = {Intersections and sums of sets for the regularization of inverse problems},
	booktitle = {Canadian Mathematical Society Winter Meeting},
	year = {2018},
	note = {(CMSWM)},
	month = {12},
	abstract = {We present new algorithms to compute projections onto the intersection of constraint sets. We focus on problems with multiple sets for which there is no simple and closed-form projection. Different from more classical methods such as Dykstra{\textquoteright}s algorithm, we do not need other algorithms to solve sub-problems. Our algorithms are based on the alternating direction method of multipliers and apply to models/images/video on small 2D and large 3D grids because we exploit computational similarity between constraint sets, coarse and fine-grained parallelism, and we also present a multilevel accelerated version. To obtain more flexible descriptions of prior knowledge, we introduce a formulation that allows constraint sets to be the sum of intersections of sets, which is essentially an extension of a Minkowski set. This formulation builds on the success of additive image descriptions that are usually based on penalty methods, such as cartoon-texture decomposition and robust principal component analysis. We show applications where we use multiple constraint sets to regularize partial-differential-equation based parameter estimation problems such as seismic waveform inversion, as well as various image and video processing and segmentation tasks.},
	keywords = {Intersections, Inverse problems, Projections, Sets},
	url = {https://cms.math.ca/Events/winter18/abs/ipi$\#$bp},
	author = {Bas Peters and Felix J. Herrmann}
}
@presentation {yang2017SINBADFiwm,
	title = {Imaging with multiples in shallow water},
	year = {2017},
	publisher = {SINBAD},
	abstract = {Based on the latest developments of research in inversion technology with optimization, researchers have made significant progress in the implementation of least-squares reverse-time migration (LS-RTM) of primaries. In Marine data however, these applications rely on the success of a pre-imaging separation of primaries and multiples, which can be modeled as a multi-dimensional convolution between the vertical derivative of the surface-free Green{\textquoteright}s function and the down-going receiver wavefield. Instead of imaging the primaries and multiples separately, we implement the LS-RTM of the total down-going wavefield by combining areal source injection and linearized Born modelling, where strong surface related multiples are generated from a strong density variation at the ocean bottom. The advantage including surface related multiples in LS-RTM is the extra illumination we obtain from these multiples without incurring additional computational costs related to carrying out multi-dimensional convolutions part of conventional multiple prediction procedures. Even though we are able to avert these computational costs, our approach shares the large costs of LS-RTM. We reduce these costs by combining randomized source subsampling with our sparsity-promoting imaging technology, which produces artifact-free, high-resolution images, with the surface-related multiples migrated properly.},
	keywords = {Presentation, SINBAD, SINBADFALL2017, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/yang2017SINBADFiwm/yang2017SINBADFiwm.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2017/Fall/yang2017SINBADFiwm/yang2017SINBADFiwm.mov},
	author = {Mengmeng Yang and Emmanouil Daskalakis and Felix J. Herrmann}
}
@conference {oghenekohwo2017EAGEitl,
	title = {Improved time-lapse data repeatability with randomized sampling and distributed compressive sensing},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2017},
	note = {(EAGE, Paris)},
	month = {06},
	abstract = {Recently, new ideas on randomized sampling for time-lapse seismic acquisition have been proposed to address some of the challenges of replicating time-lapse surveys. These ideas, which stem from distributed compressed sensing (DCS) led to the birth of a joint recovery model (JRM) for processing time-lapse data (noise-free) acquired from non-replicated acquisition geometries. However, when the earth does not change{\textendash}-i.e. no time-lapse{\textemdash}the recovered vintages from two non-replicated surveys should show high repeatability measured in terms of normalized RMS, which is a standard metric for quantifying time-lapse data repeatability. Under this assumption of no time-lapse change, we demonstrate improved repeatability (with JRM) of the recovered data from non-replicated random samplings, first with noisy data and secondly in situations where there are calibration errors i.e. where the acquisition parameters such as source/receiver coordinates are not precise.},
	keywords = {calibration, Compressive Sensing, EAGE, noise, repeatability, time lapse},
	doi = {10.3997/2214-4609.201701389},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2017/oghenekohwo2017EAGEitl/oghenekohwo2017EAGEitl.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2017/oghenekohwo2017EAGEitl/oghenekohwo2017EAGEitl_poster.pdf},
	author = {Felix Oghenekohwo and Felix J. Herrmann}
}
@presentation {wang2015SINBADFifw,
	title = {Improving full waveform inversion with spectral extrapolation},
	year = {2015},
	publisher = {SINBAD},
	abstract = {We develop a sparsity based frequency extrapolation method to obtain low frequency data from the high frequency ones. As other frequency extrapolation methods, the extrapolation introduces noise due to dispersion and possibly densely distributed reflectors. To mitigate such noise, we incorporate Curvlet coefficient regularization in the extrapolation algorithm. Numerical results demonstrate the effectiveness of the extrapolation in frequency domain FWI in models of moderate complexity.},
	keywords = {Presentation, SINBAD, SINBADFALL2015, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/wang2015SINBADFifw/wang2015SINBADFifw.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2015/Fall/wang2015SINBADFifw/wang2015SINBADFifw.mov},
	author = {Rongrong Wang and Felix J. Herrmann}
}
@conference {dasilva2015WSLRigt,
	title = {Irregular grid tensor completion},
	booktitle = {Workshop on Low-rank Optimization and Applications},
	year = {2015},
	note = {(Workshop on Low-rank Optimization and Applications, University of Bonn, Germany)},
	month = {06},
	abstract = {Low rank tensor completion has recently garnered the attention of researchers owing to the ubiquity of tensors in the sciences and the theoretical and numerical challenges compared to matrix completion. Here we consider a tensor completion scheme where the data arises from sampling a continuous function. When the sampling grid is not periodic, the resulting tensor may not be low rank in the Hierarchical Tucker sense, which can adversely affect reconstruction quality when there are missing samples. In order to compensate for this off-grid sampling, we introduce a resampling operator (here, the non-uniform Fourier transform) that accounts for this non-uniformity moreso than merely treating the sampling grid as periodic. Numerical experiments demonstrate that this approach can improve reconstruction quality when there is relatively little data.},
	keywords = {hierarchical tucker, irregular sampling, off the grid, structured tensor, tensor interpolation},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/WS_LR/2015/dasilva2015WSLRigt/dasilva2015WSLRigt_poster.pdf},
	author = {Curt Da Silva and Felix J. Herrmann}
}
@presentation {tu2014SINBADind,
	title = {Imaging the Nelson data set using surface-related multiples},
	year = {2014},
	publisher = {SINBAD},
	abstract = {We will present out latest finding on migration with multiples on the Nelson dataset.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/tu2014SINBADind/tu2014SINBADind.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@conference {herrmann2014SEGAGUWSiii,
	title = {Imaging/Inversion with irregular/random sampled spatial arrays},
	booktitle = {SEG-AGU Workshop on Advances in Active + Passive "Full Wavefield" Seismic Imaging: From Reservoirs to Plate Tectonics},
	year = {2014},
	note = {(SEG-AGU Workshop, 22-24 July, Vancouver)},
	month = {07},
	keywords = {Imaging, inversion, randomization, SEG-AGU, workshop},
	author = {Felix J. Herrmann}
}
@presentation {lin2014SINBADiit,
	title = {Implicit interpolation of trace gaps in REPSI using auto-convolution terms},
	year = {2014},
	publisher = {SINBAD},
	abstract = {It is possible to solve the Estimation of Primaries by Sparse Inversion problem from a sesimic record with 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 REPSI 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 = {Presentation, SINBAD, SINBADSPRING2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Spring/lin2014SINBADiit/lin2014SINBADiit.pdf},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@presentation {peters2014SINBADiss,
	title = {Iterative solution strategy for least-squares problem with a PDE-block},
	year = {2014},
	publisher = {SINBAD},
	abstract = {Waveform inversion using the Wavefield Reconstruction Inversion (WRI) is a quadratic-penalty based method developed in our group and has shown to have advantages over the reduced Lagrangian based conventional FWI methods. WRI involves no explicit PDE solves, but a least-squares problem with a PDE block. This type of least-squares problem is very challenging to solve using iterative methods. In this talk we show algorithms we developed specifically for this application and which involve a combination of preconditioning, low-rank decomposition and deflation.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/peters2014SINBADiss/peters2014SINBADiss.pdf},
	author = {Bas Peters and Felix J. Herrmann}
}
@presentation {zheglova2013SINBADihss,
	title = {Imaging with hierarchical semi separable matrices},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Hierarchically Semi Separable (HSS) matrices are (in general) dense matrices that have low rank off-diagonal blocks that can be represented economically. Exploiting a specific structure of HSS representation, fast algorithms have been devised for matrix matrix multiplication, addition and computing a matrix inverse. We are interested in developing fast algorithms for seismic imaging using ideas from this approach. An overview of HSS representation and some methods using HSS representations of operators will be shown in this talk.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/zheglova2013SINBADihss/zheglova2013SINBADihss.pdf},
	author = {Polina Zheglova and Felix J. Herrmann}
}
@article {mansour2013GEOPiwr,
	title = {Improved wavefield reconstruction from randomized sampling via weighted one-norm minimization},
	journal = {Geophysics},
	volume = {78},
	number = {5},
	year = {2013},
	month = {08},
	pages = {V193-V206},
	abstract = {Missing-trace interpolation aims to recover the gaps caused by physical obstacles or deliberate subsampling to control acquisition costs in otherwise regularly sampled seismic wavefields. Although transform-domain sparsity promotion has proven to be an effective tool to solve this recovery problem, current recovery techniques do not fully utilize a priori information derived from the locations of the transform-domain coefficients, especially when curvelet domain sparsity is exploited. We use recovery by weighted one-norm minimization, which exploits correlations between the locations of significant curvelet coefficients of different partitions, e.g., shot records, common-offset gathers, or frequency slices of the acquired data. We use these correlations to define a sequence of 2D curvelet-based recovery problems that exploit 3D continuity exhibited by seismic wavefields without relying on the highly redundant 3D curvelet transform. To test the performance of our weighted algorithm, we compared recoveries from different data sorting and partitioning scenarios for a seismic line from the Gulf of Suez. These tests demonstrated that our method is superior to standard $\ell_1$ minimization in terms of antialiasing capability, reconstruction quality and computational memory requirements.},
	keywords = {compressed sensing, randomized sampling, Trace interpolation, weighted one-norm minimization},
	doi = {10.1190/geo2012-0383.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2013/mansour2013GEOPiwr/mansour2013GEOPiwr.pdf},
	author = {Hassan Mansour and Felix J. Herrmann and Ozgur Yilmaz}
}
@conference {vanleeuwen2013EAGErobustFWI,
	title = {In which domain should we measure the misfit for robust full waveform inversion?},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2013},
	month = {06},
	abstract = {Full-waveform inversion relies on minimizing the difference between observed and modeled data, as measured by some penalty function. A popular choice, of course, is the least-squares penalty. However, when outliers are present in the data, the use of robust penalties such as the Huber or Student{\textquoteright}s t may significantly improve the results since they put relatively less weight on large residuals. In order for robust penalties to be effective, the outliers must be somehow localized and distinguishable from the good data. We propose to first transform the residual into a domain where the outliers are localized before measuring the misfit with a robust penalty. This is exactly how one would normally devise filters to remove the noise before applying conventional FWI. We propose to merge the two steps and let the inversion process implicitly filter out the noise. Results on a synthetic dataset show the effectiveness of the approach.},
	keywords = {EAGE, full waveform inversion},
	doi = {10.3997/2214-4609.20130839},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/vanleeuwen2013EAGErobustFWI/vanleeuwen2013EAGErobustFWI.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/vanleeuwen2013EAGErobustFWI/vanleeuwen2013EAGErobustFWI_pres.pdf},
	author = {Tristan van Leeuwen and Aleksandr Y. Aravkin and Henri Calandra and Felix J. Herrmann}
}
@article {vanderneut2013GJIirs,
	title = {Interferometric redatuming by sparse inversion},
	journal = {Geophysical Journal International},
	volume = {192},
	year = {2013},
	month = {02},
	pages = {666-670},
	abstract = {Assuming that exact transmission responses are known between the surface and a particular depth level in the subsurface, seismic sources can be effectively mapped to that level by a process called interferometric redatuming. After redatuming, the obtained wavefields can be used for imaging below this particular depth level. Interferometric redatuming consists of two steps, namely (i) the decomposition of the observed wavefields into up- and down-going constituents and (ii) a multidimensional deconvolution of the up- and downgoing wavefields. While this method works in theory, sensitivity to noise and artifacts due to incomplete acquisition call for a different formulation. In this letter, we demonstrate the benefits of formulating the two steps that undergird interferometric redatuming in terms of a transform-domain sparsity-promoting program. By exploiting compressibility of seismic wavefields in the curvelet domain, we not only become robust with respect to noise but we are also able to remove certain artifacts while preserving the frequency content. These improvements lead to a better image of the target from the redatumed data.},
	keywords = {Controlled source seismology, Interferometry, Inverse theory},
	url = {http://gji.oxfordjournals.org/content/192/2/666},
	author = {Joost van der Neut and Felix J. Herrmann}
}
@conference {tu2012SEGima,
	title = {Imaging with multiples accelerated by message passing},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {31},
	year = {2012},
	month = {11},
	pages = {1-6},
	publisher = {SEG},
	organization = {SEG},
	abstract = {With the growing realization that multiples can provide valuable information, there is a paradigm shift from removing them to using them. For instance, primary estimation by sparse inversion has demonstrated its superiority over surface-related multiple removal in many aspects. Inspired by this shift, we propose a method to image directly from the total up-going wavefield, including surface-related multiples, by sparse inversion. To address the high computational cost associated with this method, we propose to speed up the inversion by having the wave-equation solver carry out the multi-dimensional convolutions implicitly and cheaply by randomized subsampling. We improve the overall performance of this algorithm by selecting new independent copies of the randomized modeling operator, which leads to a cancellation of correlations that hamper the speed of convergence of the solver. We show the merits of our approach on a number of examples.},
	keywords = {Imaging, multiples, SEG},
	doi = {10.1190/segam2012-1552.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/tu2012SEGima/tu2012SEGima.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/tu2012SEGima/tu2012SEGima_pres.pdf},
	author = {Ning Tu and Felix J. Herrmann}
}
@conference {vanderneut2012SEGirs,
	title = {Interferometric redatuming with simultaneous and missing sources using sparsity promotion in the curvelet domain},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {31},
	year = {2012},
	month = {11},
	pages = {1-7},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Interferometric redatuming is a velocity-independent method to turn downhole receivers into virtual sources. Accurate redatuming involves solving an inverse problem, which can be highly ill-posed, especially in the presence of noise, incomplete data and limited aperture. We address these issues by combining interferometric redatuming with transform-domain sparsity promotion, leading to a formulation that deals with data imperfections. We show that sparsity promotion improves the retrieval of virtual shot records under a salt flank. To reduce acquisition costs, it can be beneficial to reduce the number of sources or shoot them simultaneously. It is shown that sparse inversion can still provide a stable solution in such cases.},
	keywords = {Imaging, Interferometry, Optimization, Processing, SEG},
	doi = {10.1190/segam2012-0566.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/vanderneut2012SEGirs/vanderneut2012SEGirs.pdf},
	author = {Joost van der Neut and Felix J. Herrmann and Kees Wapenaar}
}
@presentation {lin2012SINBADics,
	title = {An introduction to cosparse signal reconstruction},
	year = {2012},
	publisher = {SINBAD},
	abstract = {Undersampling techniques in exploration seismology usually relies on the assumption that seismic records and images permit sparse approximations under certain representations, such as Curvelet coefficients. Recent findings have suggested that for redundant representations (of which Curvelet is an example), the analysis operator that maps the physical signal to coefficients may also play a crucial role in recovering data from incomplete observations. In particular, the number of zero-valued coefficients given by the analysis operator acting on the signal, referred to as its "cosparsity", have an analogous role to the sparsity of the signal in terms of the coefficients. The cosparsity of the signal permits recovery guarantees that are completely separate from sparsity-based models, and gives rise to distinct sets of reconstruction algorithms and performances compared to sparsity-based approaches. We present in this talk some initial findings on the viability of cosparse reconstruction for a variety of seismic applications that previously relied on sparse signal reconstruction, such as data interpolation and source separation.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/lin2012SINBADics/lin2012SINBADics_pres.pdf},
	author = {Tim T.Y. Lin}
}
@presentation {aravkin2012SINBADipu,
	title = {Inverse problems using Student{\textquoteright}s t},
	year = {2012},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADSPRING2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Spring/aravkin2012SINBADipu/aravkin2012SINBADipu_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
@presentation {lin2011SINBADirEPSI,
	title = {Inside the robust EPSI formulation},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/lin2011SINBADirEPSI/lin2011SINBADirEPSI_pres.pdf},
	author = {Tim T.Y. Lin}
}
@presentation {vanderneut2011SINBADirs,
	title = {Interferometric redatuming by sparse inversion},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/vanderneut2011SINBADirs/vanderneut2011SINBADirs_pres.pdf},
	author = {Joost van der Neut}
}
@presentation {aravkin2010SINBADicc,
	title = {Introduction to convex composite optimization},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/aravkin2010SINBADicc/aravkin2010SINBADicc_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
@presentation {friedlander2010SINBADisl,
	title = {Introduction to Spot: a linear-operator toolbox},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/friedlander2010SINBADisl/friedlander2010SINBADisl_pres.pdf},
	author = {Michael P. Friedlander}
}
@mastersthesis {kumar09THins,
	title = {Incoherent noise suppression and deconvolution using curvelet-domain sparsity},
	year = {2009},
	note = {(MSc)},
	month = {06},
	school = {The University of British Columbia},
	type = {masters},
	address = {Vancouver},
	abstract = {Curvelets are a recently introduced transform domain that belongs to a family of multiscale and also multidirectional data expansions. As such, curvelets can be applied to resolution of the issues of complicated seismic wavefronts. We make use of this multiscale, multidirectional and hence sparsifying ability of the curvelet transform to suppress incoherent noise from crustal data where the signal-to-noise ratio is low and to develop an improved deconvolution procedure. Incoherent noise present in seismic reflection data corrupts the quality of the signal and can often lead to misinterpretation. The curvelet domain lends itself particularly well for denoising because coherent seismic energy maps to a relatively small number of significant curvelet coefficents.},
	keywords = {MSc},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2009/kumar09THins.pdf},
	author = {Vishal Kumar}
}
@conference {kumar2009SEGins,
	title = {Incoherent noise suppression with curvelet-domain sparsity},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {28},
	year = {2009},
	month = {10},
	pages = {3356-3360},
	publisher = {SEG},
	organization = {SEG},
	abstract = {The separation of signal and noise is a key issue in seismic data processing. By noise we refer to the incoherent noise that is present in the data. We use the recently introduced multiscale and multidirectional curvelet transform for suppression of random noise. The curvelet transform decomposes data into directional plane waves that are local in nature. The coherent features of the data occupy the large coefficients in the curvelet domain, whereas the incoherent noise lives in the small coefficients. In other words, signal and noise have minimal overlap in the curvelet domain. This gives us a chance to use curvelets to suppress noise present in data.},
	keywords = {Presentation, SEG},
	doi = {10.1190/1.3255557},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2009/kumar09SEGins/kumar09SEGins.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2009/kumar09SEGins/kumar09SEGins_pres.pdf},
	author = {Vishal Kumar and Felix J. Herrmann}
}
@conference {lin2008SEGiso,
	title = {Interpolating solutions of the Helmholtz equation with compressed sensing},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {27},
	year = {2008},
	month = {01},
	pages = {2122-2126},
	publisher = {SEG},
	organization = {SEG},
	abstract = {We present an algorithm which allows us to model wavefields with frequency-domain methods using a much smaller number of frequencies than that typically required by the classical sampling theory in order to obtain an alias-free result. The foundation of the algorithm is the recent results on the compressed sensing, which state that data can be successfully recovered from an incomplete measurement if the data is sufficiently sparse. Results from numerical experiment show that only 30\% of the total frequency spectrum is need to capture the full wavefield information when working in the hard 2D synthetic Marmousi model.},
	keywords = {Presentation, SEG, SLIM},
	doi = {10.1190/1.3059307},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2008/lin08SEGiso/lin08SEGiso.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2008/lin08SEGiso/lin08SEGiso.pdf},
	author = {Tim T.Y. Lin and Evgeniy Lebed and Yogi A. Erlangga and Felix J. Herrmann}
}
@conference {herrmann2008SINBADitc,
	title = {Introduction to compressive (wavefield) computation},
	booktitle = {SINBAD 2008},
	year = {2008},
	keywords = {Presentation, SINBAD, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2008/herrmann2008SINBADitc/herrmann2008SINBADitc.pdf},
	author = {Felix J. Herrmann and Yogi A. Erlangga and Tim T.Y. Lin and Cody R. Brown}
}
@conference {erlangga2008SEGaim,
	title = {An iterative multilevel method for computing wavefields in frequency-domain seismic inversion},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {27},
	year = {2008},
	month = {11},
	pages = {1957-1960},
	publisher = {SEG},
	organization = {SEG},
	abstract = {We describe an iterative multilevel method for solving linear systems representing forward modeling and back propagation of wavefields in frequency-domain seismic inversions. The workhorse of the method is the so-called multilevel Krylov method, applied to a multigrid-preconditioned linear system, and is called multigrid-multilevel Krylov (MKMG) method. Numerical experiments are presented for 2D Marmousi synthetic model for a range of frequencies. The convergence of the method is fast, and depends only mildly on frequency. The method can be considered as the first viable alternative to LU factorization, which is practically prohibitive for 3D seismic inversions.},
	keywords = {SEG, SLIM},
	doi = {10.1190/1.3059279},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2008/erlangga08SEGaim/erlangga08SEGaim.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2008/erlangga08SEGaim/erlangga08SEGaim_pres.pdf},
	author = {Yogi A. Erlangga and Felix J. Herrmann}
}
@conference {eso2008SEGira,
	title = {Iterative reconstruction algorithm for non-linear operators},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {27},
	year = {2008},
	month = {11},
	pages = {579-583},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Iterative soft thresholding of a models wavelet coefficients can be used to obtain models that are sparse with respect to a known basis function. We generate sparse models for non-linear forward operators by applying the soft thresholding operator to the model obtained through a Gauss-Newton iteration and apply the technique in a synthetic 2.5D DC resistivity crosswell tomographic example.},
	keywords = {SEG, SLIM},
	doi = {10.1190/1.3063719},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2008/eso08SEGira/eso08SEGira.pdf},
	author = {R. A. Eso and S. Napier and Felix J. Herrmann and D. W. Oldenburg}
}
@conference {vandenberg2007SINBADipo1,
	title = {In pursuit of a root},
	booktitle = {2007 Von Neumann Symposium},
	year = {2007},
	keywords = {minimization, Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2007/vandenberg2007SINBADipo1/vandenberg2007SINBADipo1.pdf},
	author = {Ewout van den Berg and Michael P. Friedlander}
}
@conference {vandenberg07VONipo,
	title = {In pursuit of a root},
	year = {2007},
	month = {07},
	publisher = {Von Neumann Symposium},
	organization = {Von Neumann Symposium},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/vonNeuman/2007/vandenberg07VONipo/vandenberg07VONipo.pdf},
	author = {Ewout van den Berg and Michael P. Friedlander}
}
@techreport {vandenberg07TRipr,
	title = {In pursuit of a root},
	number = {TR-EOAS-2007-19},
	year = {2007},
	month = {06},
	institution = {Department of Computer Science},
	address = {University of British Columbia, Vancouver},
	abstract = {The basis pursuit technique is used to find a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise fits the least-squares problem only approximately, and a single parameter determines a curve that traces the trade-off between the least-squares fit and the one-norm of the solution. We show that the function that describes this curve is convex and continuously differentiable over all points of interest. The dual solution of a least-squares problem with an explicit one-norm constraint gives function and derivative information needed for a root-finding method. As a result, we can compute arbitrary points on this curve. Numerical experiments demonstrate that our method, which relies on only matrix-vector operations, scales well to large problems.},
	url = {http://www.optimization-online.org/DB_HTML/2007/06/1708.html},
	author = {Ewout van den Berg and Michael P. Friedlander}
}
@conference {hennenfent2007EAGEisf,
	title = {Irregular sampling: from aliasing to noise},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2007},
	month = {06},
	abstract = {Seismic data is often irregularly and/or sparsely sampled along spatial coordinates. We show that these acquisition geometries are not necessarily a source of adversity in order to accurately reconstruct adequately-sampled data. We use two examples to illustrate that it may actually be better than equivalent regularly subsampled data. This comment was already made in earlier works by other authors. We explain this behavior by two key observations. Firstly, a noise-free underdetermined problem can be seen as a noisy well-determined problem. Secondly, regularly subsampling creates strong coherent acquisition noise (aliasing) difficult to remove unlike the noise created by irregularly subsampling that is typically weaker and Gaussian-like.},
	keywords = {EAGE, Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/hennenfent07EAGEisf/hennenfent07EAGEisf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/hennenfent07EAGEisf/hennenfent07EAGEisf_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2007/hennenfent07EAGEisf/hennenfent07EAGEisf_WS.pdf},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
@conference {moghaddam2006SINBADioa,
	title = {Imaging operator approximation using curvelets},
	booktitle = {SINBAD 2006},
	year = {2006},
	abstract = {In this presentation, the normal (demigation-migration) operator is studied in terms of a pseudo-differential operator. The invariance of curvelets under this operator and their sparsity on the seismic images is used to precondition the migration operator. A brief overview will be given on some of the theory from micro-local analysis which proofs that curvelets remain approximately invariant under the operator. The proper setting for which a diagonal approximation in the curvelet domain is accurate is discussed together with different methods that estimate this diagonal from of-the-shelf migration operators. This is joint work with Chris Stolk.},
	keywords = {Presentation, SINBAD, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2006/moghaddam2006SINBADioa/moghaddam2006SINBADioa.pdf},
	author = {Peyman P. Moghaddam}
}
