@article {louboutin2023lmi,
	title = {Learned multiphysics inversion with differentiable programming and machine learning},
	journal = {The Leading Edge},
	volume = {42},
	year = {2023},
	note = {(The Leading Edge)},
	month = {07},
	pages = {452-516},
	abstract = {We present the Seismic Laboratory for Imaging and Modeling/Monitoring (SLIM) open-source software framework for computational geophysics and, more generally, inverse problems involving the wave-equation (e.g., seismic and medical ultrasound), regularization with learned priors, and learned neural surrogates for multiphase flow simulations. By integrating multiple layers of abstraction, our software is designed to be both readable and scalable. This allows researchers to easily formulate their problems in an abstract fashion while exploiting the latest developments in high-performance computing. We illustrate and demonstrate our design principles and their benefits by means of building a scalable prototype for permeability inversion from time-lapse crosswell seismic data, which aside from coupling of wave physics and multiphase flow, involves machine learning.},
	keywords = {CCS, deep learning, Fourier neural operators, GCS, Imaging, inversion, invertible networks, machine learning, monitoring, multiphysics, Normalizing flows, SLIM, software, time-lapse},
	url = {https://library.seg.org/doi/10.1190/tle42070474.1},
	presentation = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2023/louboutin2023lmi/le_software.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2023/louboutin2023lmi/le_software.html},
	author = {Mathias Louboutin and Ziyi Yin and Rafael Orozco and Thomas J. Grady II and Ali Siahkoohi and Gabrio Rizzuti and Philipp A. Witte and Olav M{\o}yner and Gerard J. Gorman and Felix J. Herrmann}
}
@article {zhang2023otl,
	title = {Optimized time-lapse acquisition design via spectral gap ratio minimization},
	journal = {Geophysics},
	volume = {88},
	number = {4},
	year = {2023},
	note = {(Geophysics)},
	month = {07},
	pages = {A19-A23},
	abstract = {Modern-day reservoir management and monitoring of geological carbon storage increasingly call for costly time-lapse seismic data collection. In this letter, we show how techniques from graph theory can be used to optimize acquisition geometries for low-cost sparse 4D seismic. Based on midpoint-offset domain connectivity arguments, the proposed algorithm automatically produces sparse non-replicated time-lapse acquisition geometries that favor wavefield recovery.},
	keywords = {Acquisition, JRM, matrix factorization, spectral gap, survey design, time-lapse, wavefield reconstruction},
	doi = {10.1190/geo2023-0024.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2023/zhang2023otl/Spectral_Gap_Paper.html},
	author = {Yijun Zhang and Ziyi Yin and Oscar Lopez and Ali Siahkoohi and Mathias Louboutin and Rajiv Kumar and Felix J. Herrmann}
}
@article {siahkoohi2022ravi,
	title = {Reliable amortized variational inference with physics-based latent distribution correction},
	journal = {Geophysics},
	volume = {88},
	number = {3},
	year = {2023},
	note = {(Geophysics)},
	month = {05},
	abstract = {Bayesian inference for high-dimensional inverse problems is challenged by the computational costs of the forward operator and the selection of an appropriate prior distribution. Amortized variational inference addresses these challenges where a neural network is trained to approximate the posterior distribution over existing pairs of model and data. When fed previously unseen data and normally distributed latent samples as input, the pretrained deep neural network{\textendash}-in our case a conditional normalizing flow{\textendash}-provides posterior samples with virtually no cost. However, the accuracy of this approach relies on the availability of high-fidelity training data, which seldom exists in geophysical inverse problems because of the highly heterogeneous structure of the Earth. In addition, accurate amortized variational inference requires the observed data to be drawn from the training data distribution. As such, we offer a solution that increases the resilience of amortized variational inference when faced with data distribution shifts, e.g., changes in the forward model or prior distribution. Our method involves a physics-based correction to the conditional normalizing flow latent distribution to provide a more accurate approximation to the posterior distribution for the observed data at hand. To accomplish this, instead of a standard Gaussian latent distribution, we parameterize the latent distribution by a Gaussian distribution with an unknown mean and diagonal covariance. These unknown quantities are then estimated by minimizing the Kullback-Leibler divergence between the corrected and true posterior distributions. While generic and applicable to other inverse problems, by means of a seismic imaging example, we show that our correction step improves the robustness of amortized variational inference with respect to changes in number of source experiments, noise variance, and shifts in the prior distribution. This approach provides a seismic image with limited artifacts and an assessment of its uncertainty with approximately the same cost as five reverse-time migrations.},
	keywords = {Inverse problems, Normalizing flows, seismic imaging, Uncertainty quantification, Variational Inference},
	doi = {10.1190/geo2022-0472.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2023/siahkoohi2022ravi/paper.html},
	software = {https://github.com/slimgroup/ReliableAVI.jl},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Rafael Orozco and Felix J. Herrmann}
}
@article {siahkoohi2021dbif,
	title = {Deep Bayesian inference for seismic imaging with tasks},
	journal = {Geophysics},
	volume = {87},
	number = {5},
	year = {2022},
	note = {(Geophysics)},
	month = {07},
	pages = {281-302},
	abstract = {We propose to use techniques from Bayesian inference and deep neural networks to translate uncertainty in seismic imaging to uncertainty in tasks performed on the image, such as horizon tracking. Seismic imaging is an ill-posed inverse problem because of unavoidable bandwidth and aperture limitations, which that is hampered by the presence of noise and linearization errors. Many regularization methods, such as transform-domain sparsity promotion, have been designed to deal with the adverse effects of these errors, however, these methods run the risk of biasing the solution and do not provide information on uncertainty in the image space and how this uncertainty impacts certain tasks on the image. A systematic approach is proposed to translate uncertainty due to noise in the data to confidence intervals of automatically tracked horizons in the image. The uncertainty is characterized by a convolutional neural network (CNN) and to assess these uncertainties, samples are drawn from the posterior distribution of the CNN weights, used to parameterize the image. Compared to traditional priors, in the literature it is argued that these CNNs introduce a flexible inductive bias that is a surprisingly good fit for many diverse domains in imaging. The method of stochastic gradient Langevin dynamics is employed to sample from the posterior distribution. This method is designed to handle large scale Bayesian inference problems with computationally expensive forward operators as in seismic imaging. Aside from offering a robust alternative to maximum a posteriori estimate that is prone to overfitting, access to these samples allow us to translate uncertainty in the image, due to noise in the data, to uncertainty on the tracked horizons. For instance, it admits estimates for the pointwise standard deviation on the image and for confidence intervals on its automatically tracked horizons.},
	keywords = {deep priors, horizon tracking, seismic imaging, Uncertainty quantification},
	doi = {10.1190/geo2021-0666.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2022/siahkoohi2021dbif/paper.html},
	author = {Ali Siahkoohi and Gabrio Rizzuti and Felix J. Herrmann}
}
@article {sanavi2021tad,
	title = {True amplitude depth migration using curvelets},
	journal = {Geophysics},
	volume = {86},
	number = {4},
	year = {2021},
	note = {(Geophysics)},
	month = {07},
	pages = {S299-S310},
	abstract = {We have developed a true amplitude solution to the seismic imaging problem. We derive a diagonal scaling approach for the normal operator approximation in the curvelet domain. This is based on the theorem that states that curvelets remain approximately invariant under the action of the normal operator. We use curvelets as essential tools for approximation and inversion. We also exploit the theorem that states that the curvelet-domain approximation should be smooth in phase space by enforcing the smoothness of curvelet coefficients in the angle and space domains. We analyze our method using a reverse time migration-demigration code, simulating the acoustic wave equation on different synthetic models. Our method produces a good resolution with reflecting dips, reproduces the true amplitude reflectors, and compensates for incomplete illumination in seismic images.},
	keywords = {amplitude, depth migration, Imaging, inversion, LSRTM},
	doi = {10.1190/geo2019-0307.1},
	author = {Hamideh Sanavi and Peyman P. Moghaddam and Felix J. Herrmann}
}
@article {witte2019TPDedas,
	title = {An Event-Driven Approach to Serverless Seismic Imaging in the Cloud},
	journal = {IEEE Transactions on Parallel and Distributed Systems},
	volume = {31},
	number = {9},
	year = {2020},
	note = {(IEEE Transactions on Parallel and Distributed Systems)},
	month = {03},
	pages = {2032-2049},
	abstract = {Adapting the cloud for high-performance computing (HPC) is a challenging task, as software for HPC applications hinges on fast network connections and is sensitive to hardware failures. Using cloud infrastructure to recreate conventional HPC clusters is therefore in many cases an infeasible solution for migrating HPC applications to the cloud. As an alternative to the generic lift and shift approach, we consider the specific application of seismic imaging and demonstrate a serverless and event-driven pproach for running large-scale instances of this problem in the cloud. Instead of permanently running compute instances, our workflow is based on a serverless architecture with high throughput batch computing and event-driven computations, in which computational resources are only running as long as they are utilized. We demonstrate that this approach is very flexible and allows for resilient and nested levels of parallelization, including domain decomposition for solving the underlying partial differential equations. While the event-driven approach introduces some overhead as computational resources are repeatedly restarted, it inherently provides resilience to instance shut-downs and allows a significant reduction of cost by avoiding idle instances, thus making the cloud a viable alternative to on-premise clusters for large-scale seismic imaging.},
	keywords = {cloud, event-driven, Imaging, LSRTM, serverless},
	doi = {10.1109/TPDS.2020.2982626},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETPDS/2020/witte2019TPDedas/witte2019TPDedas.html},
	author = {Philipp A. Witte and Mathias Louboutin and Henryk Modzelewski and Charles Jones and James Selvage and Felix J. Herrmann}
}
@article {sharan2018fsp,
	title = {Fast sparsity-promoting microseismic source estimation},
	journal = {Geophysical Journal International},
	volume = {216},
	number = {1},
	year = {2019},
	note = {(Geophysical Journal International)},
	month = {01},
	pages = {164-181},
	abstract = {Microseismic events are generated during hydraulic fracturing of unconventional reservoirs and carry information on fracture locations and the origin times associated with these microseismic events. For drilling purposes and to prevent hazardous situations, we need to have accurate knowledge on the fracture locations as well as on their size, and their density. Because microseismic waves can travel far distances, microseismic data collected at the surface and or in boreholes can help us to monitor hydraulic fracturing. While so-called back propagation or time-reversal methods are able to focus recorded energy back onto the sources when a reasonable velocity model is available, these methods suffer from blurring especially in situations where the data acquisition suffers from lack of aperture, sparse sampling, and noise. As a result, these methods typically cannot resolve sources in close proximity, a desired feature since we need this information if we want to follow the fracture evolution in space and time. In that situation, we need to estimate the locations and the associated source-time functions for closely spaced microseismic sources along the active fractures. To overcome the limitations of time-reversal methods, we propose a wave-equation based inversion approach where we invert for the complete source wavefield in both space and time. By promoting sparsity on the source wavefield in space, we negate the effects of non-radiating sources during the inversion and obtain high-resolution intensity plots and high-fidelity estimates for the source-time functions. We obtain these results relatively fast by accelerating the linearized Bregman method with a dual formulation. Through experiments, we demonstrate that our method is computationally feasible, robust to noise, and works for closely spaced sources with overlapping source-time functions in complex geological settings.},
	keywords = {induced seismicity, Joint inversion, waveform inversion},
	doi = {10.1093/gji/ggy415},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalJournalInternational/2018/sharan2018fsp/sharan2018fsp.pdf},
	author = {Shashin Sharan and Rongrong Wang and Felix J. Herrmann}
}
@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}
}
@article {peters2018pmf,
	title = {Projection methods and applications for seismic nonlinear inverse problems with multiple constraints},
	journal = {Geophysics},
	volume = {84},
	number = {2},
	year = {2018},
	note = {(Geophysics)},
	month = {02},
	pages = {R251-R269},
	abstract = {Nonlinear inverse problems are often hampered by non-uniqueness and local minima because of missing low frequencies and far offsets in the data, lack of access to good starting models, noise, and modeling errors. A well-known approach to counter these deficiencies is to include prior information on the unknown model, which regularizes the inverse problem. While conventional regularization methods have resulted in enormous progress in ill-posed (geophysical) inverse problems, challenges remain when the prior information consists of multiple pieces. To handle this situation, we propose an optimization framework that allows us to add multiple pieces of prior information in the form of constraints. Compared to additive regularization penalties, constraints have a number of advantages making them more suitable for inverse problems such as full-waveform inversion. The proposed framework is rigorous because it offers assurances that multiple constraints are imposed uniquely at each iteration, irrespective of the order in which they are invoked. To project onto the intersection of multiple sets uniquely, we employ Dykstra{\textquoteright}s algorithm that scales to large problems and does not rely on trade-off parameters. In that sense, our approach differs substantially from approaches such as Tikhonov regularization, penalty methods, and gradient filtering. None of these offer assurances, which makes them less suitable to full-waveform inversion where unrealistic intermediate results effectively derail the iterative inversion process. By working with intersections of sets, we keep expensive objective and gradient calculations unaltered, separate from projections, and we also avoid trade-off parameters. These features allow for easy integration into existing code bases. In addition to more predictable behavior, working with constraints also allows for heuristics where we built up the complexity of the model gradually by relaxing the constraints. This strategy helps to avoid convergence to local minima that represent unrealistic models. We illustrate this unique feature with examples of varying complexity.},
	keywords = {constraints, Full-waveform inversion, intersection, Optimization, projection, regularization},
	doi = {10.1190/geo2018-0192.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2018/peters2018pmf/peters2018pmf.html},
	author = {Bas Peters and Brendan R. Smithyman and Felix J. Herrmann}
}
@article {kumar2017hrc,
	title = {Highly repeatable 3D compressive full-azimuth towed-streamer time-lapse acquisition {\textendash}- a numerical feasibility study at scale},
	journal = {The Leading Edge},
	volume = {36},
	number = {8},
	year = {2017},
	note = {(The Leading Edge)},
	month = {08},
	pages = {677-687},
	abstract = {Most conventional 3D time-lapse (or 4D) acquisitions are ocean-bottom cable (OBC) or ocean-bottom node (OBN) surveys since these surveys are relatively easy to replicate compared to towed-streamer surveys. To attain high degrees of repeatability, survey replicability and dense periodic sampling has become the norm for 4D surveys that renders this technology expensive. Conventional towed-streamer acquisitions suffer from limited illumination of subsurface due to narrow azimuth. Although, acquisition techniques such as multi-azimuth, wide-azimuth, rich-azimuth acquisition, etc., have been developed to illuminate the subsurface from all possible angles, these techniques can be prohibitively expensive for densely sampled surveys. This leads to uneven sampling, i.e., dense receiver and coarse source sampling or vice-versa, in order to make these acquisitions more affordable. Motivated by the design principles of Compressive Sensing (CS), we acquire economic, randomly subsampled (or compressive) and simultaneous towed-streamer time-lapse data without the need of replicating the surveys. We recover densely sampled time-lapse data on one and the same periodic grid by using a joint-recovery model (JRM) that exploits shared information among different time-lapse recordings, coupled with a computationally cheap and scalable rank-minimization technique. The acquisition is low cost since we have subsampled measurements (about 70\% subsampled), simulated with a simultaneous long-offset acquisition configuration of two source vessels travelling across a survey area at random azimuths. We analyze the performance of our proposed compressive acquisition and subsequent recovery strategy by conducting a synthetic, at scale, seismic experiment on a 3D time-lapse model containing geological features such as channel systems, dipping and faulted beds, unconformities and a gas cloud. Our findings indicate that the insistence on replicability between surveys and the need for OBC/OBN 4D surveys can, perhaps, be relaxed. Moreover, this is a natural next step beyond the successful CS acquisition examples discussed in this special issue.},
	keywords = {3D, CS, marine, rank minimization, simultaneous long offset, time-lapse seismic},
	doi = {10.1190/tle36080677.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2017/kumar2017hrc/kumar2017hrc.html},
	author = {Rajiv Kumar and Haneet Wason and Shashin Sharan and Felix J. Herrmann}
}
@article {shahidi2013GPars,
	title = {Application of randomized sampling schemes to curvelet-based sparsity-promoting seismic data recovery},
	journal = {Geophysical Prospecting},
	volume = {61},
	number = {5},
	year = {2013},
	month = {09},
	pages = {973-997},
	abstract = {Reconstruction of seismic data is routinely used to improve the quality and resolution of seismic data from incomplete acquired seismic recordings. Curvelet-based Recovery by Sparsity-promoting Inversion, adapted from the recently-developed theory of compressive sensing, is one such kind of reconstruction, especially good for recovery of undersampled seismic data. Like traditional Fourier-based methods, it performs best when used in conjunction with randomized subsampling, which converts aliases from the usual regular periodic subsampling into easy-to-eliminate noise. By virtue of its ability to control gap size, along with the random and irregular nature of its sampling pattern, jittered (sub)sampling is one proven method that has been used successfully for the determination of geophone positions along a seismic line. In this paper, we extend jittered sampling to two-dimensional acquisition design, a more difficult problem, with both underlying Cartesian, and hexagonal grids. We also study what we term separable and non-separable two-dimensional jittered samplings. We find hexagonal jittered sampling performs better than Cartesian jittered sampling, while fully non-separable jittered sampling performs better than separable jittered sampling. Two other 2D randomized sampling methods, Poisson Disk sampling and Farthest Point sampling, both known to possess blue-noise spectra, are also shown to perform well.},
	keywords = {curvelets, Geophysical Prospecting, randomized sampling},
	doi = {10.1111/1365-2478.12050},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2013/shahidi2013GPars/shahidi2013GPars.pdf},
	author = {Reza Shahidi and Gang Tang and Jianwei Ma and Felix J. Herrmann}
}
@article {herrmann2013TLEffwi,
	title = {Frugal full-waveform inversion: from theory to a practical algorithm},
	journal = {The Leading Edge},
	volume = {32},
	number = {9},
	year = {2013},
	month = {09},
	pages = {1082-1092},
	abstract = {As conventional oil and gas fields are maturing, our profession is challenged to come up with the next-generation of more and more sophisticated exploration tools. In exploration seismology this trend has led to the emergence of wave-equation based inversion technologies such as reverse-time migration and full-waveform inversion. While significant progress has been made in wave-equation based inversion, major challenges remain in the development of robust and computationally feasible workflows that give reliable results in geophysically challenging areas that may include ultra-low shear velocity zones or high-velocity salt. Moreover, sub-salt production carries risks that needs mitigation, which raises the bar from creating sub-salt images to inverting for sub-salt overpressure.},
	keywords = {Optimization, waveform inversion},
	doi = {10.1190/tle32091082.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/TheLeadingEdge/2013/herrmann2013ffwi/herrmann2013ffwi.html},
	author = {Felix J. Herrmann and Andrew J. Calvert and Ian Hanlon and Mostafa Javanmehri and Rajiv Kumar and Tristan van Leeuwen and Xiang Li and Brendan R. Smithyman and Eric Takam Takougang and Haneet Wason}
}
@article {Friedlander11TRhdm,
	title = {Hybrid deterministic-stochastic methods for data fitting},
	journal = {SIAM Journal on Scientific Computing},
	volume = {34},
	number = {3},
	year = {2012},
	month = {01},
	pages = {A1380-A1405},
	abstract = {Many structured data-fitting applications require the solution of an optimization problem involving a sum over a potentially large number of measurements. Incremental gradient algorithms (both deterministic and randomized) offer inexpensive iterations by sampling only subsets of the terms in the sum. These methods can make great progress initially, but often slow as they approach a solution. In contrast, full gradient methods achieve steady convergence at the expense of evaluating the full objective and gradient on each iteration. We explore hybrid methods that exhibit the benefits of both approaches. Rate of convergence analysis and numerical experiments illustrate the potential for the approach.},
	keywords = {Optimization},
	doi = {10.1137/110830629},
	author = {Michael P. Friedlander and Mark Schmidt}
}
@article {mansour2012IEEETITrcs,
	title = {Recovering compressively sampled signals using partial support information},
	journal = {IEEE Transactions on Information Theory},
	volume = {58},
	number = {2},
	year = {2012},
	month = {02},
	pages = {1122-1134},
	publisher = {Department of Computer Science},
	address = {University of British Columbia, Vancouver},
	abstract = {We study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50\% of the (partial) support information is accurate, then weighted $\ell_1$ minimization is stable and robust under weaker sufficient conditions than the analogous conditions for standard $\ell_1$ minimization. Moreover, weighted $\ell_1$ minimization provides better upper bounds on the reconstruction error in terms of the measurement noise and the compressibility of the signal to be recovered. We illustrate our results with extensive numerical experiments on synthetic data and real audio and video signals.},
	keywords = {Compressive Sensing},
	doi = {10.1109/TIT.2011.2167214},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETransInformationTheory/2012/mansour2012IEEETITrcs/mansour2012IEEETITrcs.pdf},
	author = {Michael P. Friedlander and Hassan Mansour and Rayan Saab and Ozgur Yilmaz}
}
@article {saab2008ACHAsrb,
	title = {Sparse recovery by non-convex optimization - instance optimality},
	journal = {Applied and Computational Harmonic Analysis},
	volume = {29},
	number = {1},
	year = {2010},
	month = {07},
	pages = {30-48},
	abstract = {In this note, we address the theoretical properties of $\Delta_p$, a class of compressed sensing decoders that rely on $l^p$ minimization with $p \in (0,1)$ to recover estimates of sparse and compressible signals from incomplete and inaccurate measurements. In particular, we extend the results of Cand{\textquoteleft}es, Romberg and Tao [3] and Wojtaszczyk [30] regarding the decoder $\Delta_1$, based on $\ell^1$ minimization, to $Δp$ with $p \in (0,1)$. Our results are two-fold. First, we show that under certain sufficient conditions that are weaker than the analogous sufficient conditions for $\Delta_1$ the decoders $\Delta_p$ are robust to noise and stable in the sense that they are $(2,p)$ instance optimal. Second, we extend the results of Wojtaszczyk to show that, like $\Delta_1$, the decoders $\Delta_p$ are (2,2) instance optimal in probability provided the measurement matrix is drawn from an appropriate distribution. While the extension of the results of [3] to the setting where $p \in (0,1)$ is straightforward, the extension of the instance optimality in probability result of [30] is non-trivial. In particular, we need to prove that the $LQ_1$ property, introduced in [30], and shown to hold for Gaussian matrices and matrices whose columns are drawn uniformly from the sphere, generalizes to an $LQ_p$ property for the same classes of matrices. Our proof is based on a result by Gordon and Kalton [18] about the Banach-Mazur distances of p-convex bodies to their convex hulls.},
	keywords = {Compressive Sensing, non-convex},
	doi = {10.1016/j.acha.2009.08.002},
	url = {http://www.sciencedirect.com/science/article/pii/S1063520309000864},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/ACHA/2010/saab2008ACHAsrb/saab2008ACHAsrb.pdf},
	author = {Rayan Saab and Ozgur Yilmaz}
}
@article {vandenberg2009ACMstf,
	title = {Sparco: a testing framework for sparse reconstruction},
	journal = {ACM Transactions on Mathematical Software},
	volume = {35},
	number = {4},
	year = {2009},
	month = {02},
	pages = {1-16},
	abstract = {Sparco is a framework for testing and benchmarking algorithms for sparse reconstruction. It includes a large collection of sparse reconstruction problems drawn from the imaging, compressed sensing, and geophysics literature. Sparco is also a framework for implementing new test problems and can be used as a tool for reproducible research. Sparco is implemented entirely in Matlab, and is released as open-source software under the GNU Public License.},
	keywords = {compressed sensing, linear operators, Sparse recovery},
	url = {http://doi.acm.org/10.1145/1462173.1462178},
	author = {Ewout van den Berg and Michael P. Friedlander and Gilles Hennenfent and Felix J. Herrmann and Rayan Saab and Ozgur Yilmaz}
}
@article {wang2008GEOPbws,
	title = {Bayesian wavefield separation by transform-domain sparsity promotion},
	journal = {Geophysics},
	volume = {73},
	number = {5},
	year = {2008},
	month = {07},
	pages = {1-6},
	abstract = {Successful removal of coherent noise sources greatly determines the quality of seismic imaging. Major advances were made in this direction, e.g., Surface-Related Multiple Elimination (SRME) and interferometric ground-roll removal. Still, moderate phase, timing, amplitude errors and clutter in the predicted signal components can be detrimental. Adopting a Bayesian approach along with the assumption of approximate curvelet-domain independence of the to-be-separated signal components, we construct an iterative algorithm that takes the predictions produced by for example SRME as input and separates these components in a robust fashion. In addition, the proposed algorithm controls the energy mismatch between the separated and predicted components. Such a control, which was lacking in earlier curvelet-domain formulations, produces improved results for primary-multiple separation on both synthetic and real data.},
	keywords = {curvelet transform, Geophysics, Optimization, Processing, SLIM},
	doi = {10.1190/1.2952571},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/wang08GEObws/wang08GEObws.pdf},
	html_version = {https://slim.gatech.edu/Publications/Public/Journals/2008/wang08TRbss/paper_html/paper.html},
	author = {Deli Wang and Rayan Saab and Ozgur Yilmaz and Felix J. Herrmann}
}
@article {herrmann2008ACHAsac,
	title = {Sparsity- and continuity-promoting seismic image recovery with curvelet frames},
	journal = {Applied and Computational Harmonic Analysis},
	volume = {24},
	number = {2},
	year = {2008},
	month = {03},
	pages = {150-173},
	abstract = {A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. We observe that curvelets, as a directional frame expansion, lead to sparsity of seismic images and exhibit invariance under the normal operator of the linearized imaging problem. Based on this observation we derive a method for stable recovery of the migration amplitudes from noisy data. The method corrects the amplitudes during a post-processing step after migration, such that the main additional cost is one ap- plication of the normal operator, i.e. a modeling followed by a migration. Asymptotically this normal operator corresponds to a pseudodifferential operator, for which a convenient diagonal approximation in the curvelet domain is derived, including a bound for its error and a method for the estimation of the diagonal from a compound operator consisting of discrete implementations for the scattering operator and its adjoint the migration operator. The solution is formulated as a nonlinear optimization problem where sparsity in the curvelet domain as well as continuity along the imaged reflectors are jointly promoted. To enhance sparsity, the $ell_1$-norm on the curvelet coefficients is minimized, while continuity is promoted by minimizing an anisotropic diffusion norm on the image. The performance of the recovery scheme is evaluated with a time-reversed {\textquoteright}wave-equation{\textquoteright} migration code on synthetic datasets, including the complex SEG/EAGE AA salt model.},
	keywords = {curvelet transform, Imaging, Processing, SLIM},
	doi = {10.1016/j.acha.2007.06.007},
	url = {https://slim.gatech.edu/Publications/Public/Journals/ACHA/2008/herrmann2008ACHAsac/herrmann2008ACHAsac.pdf},
	author = {Felix J. Herrmann and Peyman P. Moghaddam and Christiaan C. Stolk}
}
@article {friedlander2007TASdtd,
	title = {Discussion: the Dantzig selector: statistical estimation when p is much larger than n},
	journal = {The Annals of Statistics},
	volume = {35},
	number = {6},
	year = {2007},
	month = {03},
	pages = {2385-2391},
	keywords = {dantzig, SLIM, statistics},
	doi = {10.1214/009053607000000479},
	author = {Michael P. Friedlander and M. A. Saunders}
}
