@article {liu2018ssi,
	title = {Simultaneous-shot inversion for PDE-constrained optimization problems with missing data},
	journal = {Inverse Problems},
	volume = {35},
	number = {2},
	year = {2018},
	note = {(Inverse Problems)},
	pages = {025003},
	abstract = {Stochastic optimization is key to efficient inversion in PDE-constrained optimization. Using {\textquoteleft}simultaneous shots{\textquoteright}, or random superposition of source terms, works very well in simple acquisition geometries where all sources see all receivers, but this rarely occurs in practice. We develop an approach that interpolates data to an ideal acquisition geometry while solving the inverse problem using simultaneous shots. The approach is formulated as a joint inverse problem, combining ideas from low-rank interpolation with full-waveform inversion. Results using synthetic experiments illustrate the flexibility and efficiency of the approach.},
	keywords = {Full-waveform inversion, low-rank interpolation, Optimization},
	doi = {10.1088/1361-6420/aaf317},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InverseProblems/2018/liu2018ssi/liu2018ssi.pdf},
	author = {Michelle Liu and Rajiv Kumar and Eldad Haber and Aleksandr Y. Aravkin}
}
@article {esser2016tvr,
	title = {Total-variation regularization strategies in full-waveform inversion},
	journal = {SIAM Journal on Imaging Sciences},
	volume = {11},
	number = {1},
	year = {2018},
	note = {(SIAM Journal on Imaging Sciences)},
	pages = {376-406},
	abstract = {We propose an extended full-waveform inversion formulation that includes general convex constraints on the model. Though the full problem is highly nonconvex, the overarching optimization scheme arrives at geologically plausible results by solving a sequence of relaxed and warm-started constrained convex subproblems. The combination of box, total-variation, and successively relaxed asymmetric total-variation constraints allows us to steer free from parasitic local minima while keeping the estimated physical parameters laterally continuous and in a physically realistic range. For accurate starting models, numerical experiments carried out on the challenging 2004 BP velocity benchmark demonstrate that bound and total-variation constraints improve the inversion result significantly by removing inversion artifacts, related to source encoding, and by clearly improved delineation of top, bottom, and flanks of a high-velocity high-contrast salt inclusion. The experiments also show that for poor starting models these two constraints by themselves are insufficient to detect the bottom of high-velocity inclusions such as salt. Inclusion of the one-sided asymmetric total-variation constraint overcomes this issue by discouraging velocity lows to buildup during the early stages of the inversion. To the author{\textquoteright}s knowledge the presented algorithm is the first to successfully remove the imprint of local minima caused by poor starting models and band-width limited finite aperture data.},
	keywords = {constrained optimization, Full-waveform inversion, hinge loss, salt, total variation},
	doi = {10.1137/17M111328X},
	url = {https://slim.gatech.edu/Publications/Public/Journals/SIAMJournalOnImagingSciences/2018/esser2016tvr/esser2016tvr.pdf},
	url2 = {https://doi.org/10.1137/17M111328X},
	author = {Ernie Esser and Llu{\'\i}s Guasch and Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@article {kumar2016bls,
	title = {Beating level-set methods for 5D seismic data interpolation: a primal-dual alternating approach},
	journal = {IEEE Transactions on Computational Imaging},
	year = {2017},
	note = {(published online in IEEE Transactions on Computational Imaging)},
	month = {04},
	abstract = {Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to {\textquoteright}fill in{\textquoteright} data volumes from critically subsampled data acquired in the field. Tremendous size of seismic data volumes required for seismic processing remains a major challenge for these techniques. Residual-constrained formulations require less parameter tuning when the target noise floor is known. We propose a new approach to solve residual constrained formulations for interpolation. We represent the data volume in a compressed manner using low-rank matrix factors, and build a block-coordinate algorithm with constrained convex subproblems that are solved with a primal-dual splitting scheme. The develop optimization framework works on the whole seismic temporal frequency slices and does not require windowing or non-trivial sorting of seismic data. The new approach is competitive with state of the art level-set algorithms that interchange the role of objectives with constraints. We use the new algorithm to successfully interpolate a large scale 5D seismic data volume (upto 1010 data-points), generated from the geologically complex synthetic 3D Compass velocity model, where 80\% of the data has been removed. We also develop a robust extension of the primal-dual approach to deal with the outliers (or noise) in the data.},
	keywords = {alternating minimization, matrix completion, primal-dual splitting, seismic data, seismic trace interpolation},
	doi = {10.1109/TCI.2017.2693966},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETransComputationalImaging/2017/kumar2016bls/kumar2016bls.pdf},
	author = {Rajiv Kumar and Oscar Lopez and Damek Davis and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@article {tu2015GJIsem,
	title = {Source estimation with surface-related multiples{\textendash}-fast ambiguity-resolved seismic imaging},
	journal = {Geophysical Journal International},
	volume = {205},
	year = {2016},
	note = {(published online in Geophysical Journal International)},
	month = {03},
	pages = {1492-1511},
	abstract = {We address the problem of obtaining a reliable seismic image without prior knowledge of the source wavelet, especially from data that contain strong surface-related multiples. Conventional reverse-time migration requires prior knowledge of the source wavelet, which is either technically or computationally challenging to accurately determine; inaccurate estimates of the source wavelet can result in seriously degraded reverse-time migrated images, and therefore wrong geological interpretations. To solve this problem, we present a "wavelet-free" imaging procedure that simultaneously inverts for the source wavelet and the seismic image, by tightly integrating source estimation into a fast least-squares imaging framework, namely compressive imaging, given a reasonably accurate background velocity model. However, this joint inversion problem is difficult to solve as it is plagued with local minima and the ambiguity with respect to amplitude scalings because of the multiplicative, and therefore nonlinear, appearance of the source wavelet in the otherwise linear formalism. We have found a way to solve this nonlinear joint-inversion problem using a technique called variable projection, and a way to overcome the scaling ambiguity by including surface-related multiples in our imaging procedure following recent developments in surface-related multiple prediction by sparse inversion. As a result, we obtain without prior knowledge of the source wavelet high-resolution seismic images, comparable in quality to images obtained assuming the true source wavelet is known. By leveraging the computationally efficient compressive-imaging methodology, these results are obtained at affordable computational costs compared with conventional processing work flows that include surface-related multiple removal and reverse-time migration.},
	keywords = {computational seismology, free surface, Inverse theory, multiples, seismic imaging, time series analysis, wave propagation},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalJournalInternational/2016/tu2015GJIsem/tu2015GJIsem.pdf},
	url2 = {http://gji.oxfordjournals.org/content/205/3/1492.full.pdf?keytype=ref\&ijkey=zFydRGQpiJzeCS9},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Tim T.Y. Lin and Felix J. Herrmann}
}
@conference {esser2015SEGasd,
	title = {Automatic salt delineation {\textendash}- Wavefield Reconstruction Inversion with convex constraints},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2015},
	note = {(SEG, New Orleans)},
	month = {10},
	pages = {1337-1343},
	abstract = {We extend full-waveform inversion by Wavefield Reconstruction Inversion by including convex constraints on the model. Contrary to the conventional adjoint-state formulations, Wavefield Reconstruction Inversion has the advantage that the Gauss-Newton Hessian is well approximated by a diagonal scaling, which allows us to add convex constraints, such as the box- and the edge-preserving total-variation constraint, on the square slowness without incurring significant increases in computational costs. As the examples demonstrate, including these constraints yields far superior results in complex geological areas that contain high-velocity high-contrast bodies (e.g. salt or basalt). Without these convex constraints, adjoint-state and Wavefield Reconstruction Inversion get trapped in local minima for poor starting models.},
	keywords = {convex constraints, Full-waveform inversion, salt, SEG, total-variation norm},
	doi = {10.1190/segam2015-5877995.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2015/esser2015SEGasd/esser2015SEGasd.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2015/esser2015SEGasd/esser2015SEGasd_pres.pdf},
	author = {Ernie Esser and Llu{\'\i}s Guasch and Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@article {kumar2014GEOPemc,
	title = {Efficient matrix completion for seismic data reconstruction},
	journal = {Geophysics},
	volume = {80},
	number = {5},
	year = {2015},
	note = {(Geophysics)},
	month = {09},
	pages = {V97-V114},
	abstract = {Despite recent developments in improved acquisition, seismic data often remain undersampled along source and receiver coordinates, resulting in incomplete data for key applications such as migration and multiple prediction. We have interpreted the missing-trace interpolation problem in the context of matrix completion (MC), and developed three practical principles for using low-rank optimization techniques to recover seismic data. Specifically, we strive for recovery scenarios wherein the original signal is low rank and the subsampling scheme increases the singular values of the matrix. We use an optimization program that restores this low-rank structure to recover the full volume. Omitting one or more of these principles can lead to poor interpolation results, as we found experimentally. In light of this theory, we compensate for the high-rank behavior of data in the source-receiver domain by using the midpoint-offset transformation for 2D data and a source-receiver permutation for 3D data to reduce the overall singular values. Simultaneously, to work with computationally feasible algorithms for large-scale data, we use a factorization-based approach to MC, which significantly speeds up the computations compared with repeated singular value decompositions without reducing the recovery quality. In the context of our theory and experiments, we also find that windowing the data too aggressively can have adverse effects on the recovery quality. To overcome this problem, we carried out our interpolations for each frequency independently while working with the entire frequency slice. The result is a computationally efficient, theoretically motivated framework for interpolating missing-trace data. Our tests on realistic 2D and 3D seismic data sets show that our method compares favorably in terms of computational speed and recovery quality with existing curvelet- and tensor-based techniques.},
	keywords = {2D, 3D, algorithm, interpolation, low-rank, signal processing},
	doi = {10.1190/geo2014-0369.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2015/kumar2014GEOPemc/kumar2014GEOPemc.pdf},
	url2 = {http://library.seg.org/doi/abs/10.1190/geo2014-0369.1},
	author = {Rajiv Kumar and Curt Da Silva and Okan Akalin and Aleksandr Y. Aravkin and Hassan Mansour and Ben Recht and Felix J. Herrmann}
}
@conference {kumar2015IIPFWIrmb,
	title = {Rank minimization based seismic data processing and inversion},
	booktitle = {Inaugural Full-Waveform Inversion Workshop},
	year = {2015},
	note = {(Natal, Brazil)},
	month = {08-09},
	abstract = {We present the low-rank extensions of full-waveform inversion to mitigate the local-minima issues. The purpose formulation is computationally tractable and does not involve any extra computational cost compared to the adjoint-state method.},
	keywords = {FWI, inversion, Processing, rank minimization},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/IIPFWI/kumar2015IIPFWIrmb/kumar2015IIPFWIrmb_pres.pdf},
	author = {Rajiv Kumar and Curt Da Silva and Oscar Lopez and Aleksandr Y. Aravkin and Hassan Mansour and Haneet Wason and Ernie Esser and Felix J. Herrmann}
}
@techreport {esser2015tvwri,
	title = {Total variation regularization strategies in full waveform inversion for improving robustness to noise, limited data and poor initializations},
	number = {TR-EOAS-2015-5},
	year = {2015},
	month = {06},
	institution = {UBC},
	abstract = {We propose an extended full waveform inversion formulation that includes convex constraints on the model. In particular, we show how to simultaneously constrain the total variation of the slowness squared while enforcing bound constraints to keep it within a physically realistic range. Synthetic experiments show that including total variation regularization can improve the recovery of a high velocity perturbation to a smooth background model, removing artifacts caused by noise and limited data. Total variation-like constraints can make the inversion results significantly more robust to a poor initial model, leading to reasonable results in some cases where unconstrained variants of the method completely fail. Numerical results are presented for portions of the SEG/EAGE salt model and the 2004 BP velocity benchmark. ***Disclaimer.*** *This technical report is ongoing work (and posted as is except for the addition of another author) of the late John "Ernie" Esser (May 19, 1980 - March 8, 2015), who passed away under tragic circumstances. We will work hard to finalize and submit this work to the peer-review literature.* Felix J. Herrmann},
	keywords = {cones constraints, hinge loss, total-variation, Wavefield Reconstruction Inversion},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2015/esser2015tvwri/esser2015tvwri.html},
	author = {Ernie Esser and Llu{\'\i}s Guasch and Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@article {vanLeeuwen2014GEOPcav,
	title = {Comment on: {\textquotedblleft}Application of the variable projection scheme for frequency-domain full-waveform inversion{\textquotedblright} (M. Li, J. Rickett, and A. Abubakar, Geophysics, 78, no. 6, R249{\textendash}R257)},
	journal = {Geophysics},
	volume = {79},
	number = {3},
	year = {2014},
	note = {(discussion by Tristan van Leeuwen, Aleksandr Y. Aravkin, and Felix J. Herrmann)},
	month = {05},
	pages = {X11-X17},
	keywords = {variable projection, waveform inversion},
	doi = {10.1190/geo2013-0466.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2014/vanLeeuwen2014GEOPcav/vanLeeuwen2014GEOPcav.pdf},
	author = {Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@presentation {tu2014SINBADfis2,
	title = {Fast imaging with source estimation},
	year = {2014},
	publisher = {SINBAD},
	abstract = {In seismic imaging, an inaccurate estimate of the source wavelet may result in degraded seismic images. While conventional reverse-time migration requires the knowledge of the source wavelet as prior information, we propose to include source estimation in the fast compressive imaging procedure. Using the proposed method, we can obtain seismic images that are comparable to those imaged with the true source wavelet, with computational costs that are comparable to conventional RTM images with all the data. We also extend the proposed method to image data with surface-related multiples, where these multiples help to mitigate the amplitude ambiguity in source estimation. We verify the proposed method using realistic synthetic examples.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/tu2014SINBADfis2/tu2014SINBADfis2.pdf},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Tim T.Y. Lin and Felix J. Herrmann}
}
@article {aravkin2014SISCfmd,
	title = {Fast methods for denoising matrix completion formulations, with applications to robust seismic data interpolation},
	journal = {SIAM Journal on Scientific Computing},
	volume = {36},
	number = {5},
	year = {2014},
	note = {(SISC)},
	month = {10},
	pages = {S237-S266},
	abstract = {Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of rows and columns, paving the way for matrix completion in extremely large-scale applications, such as seismic data interpolation. In this paper, we consider matrix completion formulations designed to hit a target data-fitting error level provided by the user, and we propose an algorithm called LR-BPDN that is able to exploit factorized formulations to solve the corresponding optimization problem. Since practitioners typically have strong prior knowledge about target error level, this innovation makes it easy to apply the algorithm in practice, leaving only the factor rank to be determined. Within the established framework, we propose two extensions that are highly relevant to solving practical challenges of data interpolation. First, we propose a weighted extension that allows known subspace information to improve the results of matrix completion formulations. We show how this weighting can be used in the context of frequency continuation, an essential aspect to seismic data interpolation. Second, we propose matrix completion formulations that are robust to large measurement errors in the available data. We illustrate the advantages of LR-BPDN on collaborative filtering problems using the MovieLens 1M and 10M and Netflix 100M datasets. Then we use the new method, along with its robust and subspace reweighted extensions, to obtain high-quality reconstructions for large-scale seismic interpolation problems with real data, even in the presence of data contamination.},
	keywords = {factorized formulations, matrix completion, robust statistics, seismic trace interpolation, variational optimization},
	doi = {10.1137/130919210},
	url = {https://slim.gatech.edu/Publications/Public/Journals/SIAMJournalOnScientificComputing/2014/aravkin2014SISCfmd/aravkin2014SISCfmd.pdf},
	url2 = {http://epubs.siam.org/doi/abs/10.1137/130919210},
	author = {Aleksandr Y. Aravkin and Rajiv Kumar and Hassan Mansour and Ben Recht and Felix J. Herrmann}
}
@techreport {esser2014SEGsgp,
	title = {A scaled gradient projection method for total variation regularized full waveform inversion},
	number = {TR-EOAS-2014-2},
	year = {2014},
	month = {04},
	institution = {UBC},
	abstract = {We propose an extended full waveform inversion formulation that includes convex constraints on the model. In particular, we show how to simultaneously constrain the total variation of the slowness squared while enforcing bound constraints to keep it within a physically realistic range. Synthetic experiments show that including total variation regularization can improve the recovery of a high velocity perturbation to a smooth background model.},
	keywords = {convex constraints, full waveform inversion, total variation regularization},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/esser2014SEGsgp/esser2014SEGsgp.html},
	author = {Ernie Esser and Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@presentation {esser2014SINBADsgp,
	title = {A scaled gradient projection method for total variation regularized full waveform inversion},
	year = {2014},
	publisher = {SINBAD},
	abstract = {We propose a modification to the quadratic penalty formulation for seismic full waveform inversion proposed by van Leeuwen and Herrmann that includes convex constraints on the model. In particular, we show how to simultaneously constrain the total variation of the slowness squared while enforcing bound constraints to keep it within a physically realistic range. Synthetic experiments show that including total variation regularization can improve the recovery of a high velocity perturbation to a smooth background model.},
	keywords = {Presentation, SINBAD, SINBADSPRING2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Spring/esser2014SINBADsgp/esser2014SINBADsgp.pdf},
	author = {Ernie Esser and Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@conference {wason2014SEGsss,
	title = {Source separation via SVD-free rank minimization in the hierarchical semi-separable representation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2014},
	note = {(SEG)},
	month = {10},
	pages = {120-126},
	abstract = {Recent developments in matrix rank optimization have allowed for new computational approaches in the field of source separation or deblending. In this paper, we propose a source separation algorithm for blended marine acquisition, where two sources are deployed at different depths (over/under acquisition). The separation method incorporates the Hierarchical Semi-Separable structure (HSS) inside rank-regularized least-squares formulations. The proposed approach is suitable for large scale problems, since it avoids SVD computations and uses a low-rank factorized formulation instead. We illustrate the performance of the new HSS-based deblending approach by simulating an over/under blended acquisition, wherein uniformly random time delays (of < 1 second) are applied to one of the sources.},
	keywords = {Acquisition, deblending, HSS, marine, Rank, SEG, source separation},
	doi = {http://dx.doi.org/10.1190/segam2014-1583.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/wason2014SEGsss/wason2014SEGsss.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2014/wason2014SEGsss/wason2014SEGsss_pres.pdf},
	author = {Haneet Wason and Rajiv Kumar and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@conference {kumar2014EAGErank,
	title = {SVD-free low-rank matrix factorization : wavefield reconstruction via jittered subsampling and reciprocity},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2014},
	month = {06},
	abstract = {Recently computationally efficient rank optimization techniques have been studied extensively to develop a new mathematical tool for the seismic data interpolation. So far, matrix completion problems have been discussed where sources are subsample according to a discrete uniform distribution. In this paper, we studied the effect of two different subsampling techniques on seismic data interpolation using rank-regularized formulations, namely jittered subsampling over uniform random subsampling. The other objective of this paper is to combine the fact of source-receiver reciprocity with the rank-minimization techniques to enhance the accuracy of missing-trace interpolation. We illustrate the advantages of jittered subsampling and reciprocity using a seismic line from Gulf of Suez to obtain high quality results for interpolation, a key application in exploration geophysics.},
	keywords = {EAGE, interpolation, low-rank, reciprocity},
	doi = {10.3997/2214-4609.20141394},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/kumar2014EAGErank/kumar2014EAGErank.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2014/kumar2014EAGErank/kumar2014EAGErank_pres.pdf},
	author = {Rajiv Kumar and Aleksandr Y. Aravkin and Ernie Esser and Hassan Mansour and Felix J. Herrmann}
}
@presentation {esser2014SINBADtvc,
	title = {Total variation constrained full waveform inversion with continuation},
	year = {2014},
	publisher = {SINBAD},
	abstract = {Adding a total variation constraint to the Wavefield Reconstruction Inversion model proposed by van Leeuwen and Herrmann can improve robustness and remove artifacts by encouraging piecewise smooth solutions. However, if the parameter controlling the strength of the TV regularization is not well chosen, important details can be lost. We investigate continuation strategies that gradually reduce the strength of the TV constraint so that these important details are eventually allowed back into the solution. Preliminary numerical experiments suggest that this can improve the solution path and lead to better velocity models than if TV regularization were not used during the intermediate steps.},
	keywords = {Presentation, SINBAD, SINBADFALL2014, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2014/Fall/esser2014SINBADtvc/esser2014SINBADtvc.pdf},
	author = {Ernie Esser and Llu{\'\i}s Guasch and Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@presentation {tu2013SINBADvp,
	title = {Fast imaging with multiples and source estimation},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Multiples are usually treated as unwanted components in seismic data. However, if correctly used, they can provide valuable information about the subsurface. In this presentation, I will talk about how to make use of multiples in $\ell_1$ regularized least-squares imaging, and how to estimate the source wavelet on the fly using multiples. Synthetic examples show that using multiples not only helps to retrieve the true-amplitude seismic image and the source wavelet, it also increases the wavenumber contents in the seismic image. By using dimensionality reduction techniques with rerandomization, we also greatly decrease the simulation cost without compromising the image quality.},
	keywords = {Presentation, SINBAD, SINBADSPRING2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Spring/tu2013SINBADvp/tu2013SINBADvp.pdf},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {tu2013EAGElsm,
	title = {Fast least-squares migration with multiples and source estimation},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2013},
	month = {06},
	abstract = {The advent of modern computing has made it possible to do seismic imaging using least-squares reverse-time migration. We obtain superior images by solving an optimization problem that recovers the true-amplitude images. However, its success hinges on overcoming several issues, including overwhelming problem size, unknown source wavelet, and interfering coherent events like multiples. In this abstract, we reduce the problem size by using ideas from compressive sensing, and estimate source wavelet by generalized variable projection. We also demonstrate how to invert for subsurface information encoded in surface-related multiples by incorporating the free-surface operator as an areal source in reverse-time migration. Our synthetic examples show that multiples help to improve the resolution of the image, as well as remove the amplitude ambiguity in wavelet estimation.},
	keywords = {EAGE, Imaging, multiples, source estimation, sparse},
	doi = {10.3997/2214-4609.20130727},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/tu2013EAGElsm/tu2013EAGElsm.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/tu2013EAGElsm/tu2013EAGElsm_pres.pdf},
	author = {Ning Tu and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@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}
}
@conference {kumar2013SEGHSS,
	title = {Reconstruction of seismic wavefields via low-rank matrix factorization in the hierarchical-separable matrix representation},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {32},
	year = {2013},
	month = {09},
	pages = {3628-3633},
	abstract = {Recent developments in matrix rank optimization have allowed for new computational approaches in the field of seismic data interpolation. In this paper, we propose an approach for seismic data interpolation which incorporates the Hierarchical Semi-Separable Structure (HSS) inside rank-regularized least-squares formulations for the missing-trace interpolation problem. The proposed approach is suitable for large scale problems, since it avoids SVD computations and uses a low-rank factorized formulation instead. We illustrate the advantages of the new HSS approach by interpolating a seismic line from the Gulf of Suez and compare the reconstruction with conventional rank minimization.},
	keywords = {HSS, interpolation, SEG},
	doi = {10.1190/segam2013-1165.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/kumar2013SEGHSS/kumar2013SEGHSS.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/kumar2013SEGHSS/kumar2013SEGHSS_pres.pdf},
	author = {Rajiv Kumar and Hassan Mansour and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@conference {kumar2013EAGEsind,
	title = {Seismic data interpolation and denoising using SVD-free low-rank matrix factorization},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2013},
	month = {06},
	abstract = {Recent developments in rank optimization have allowed new approaches for seismic data interpolation and denoising. In this paper, we propose an approach for simultaneous seismic data interpolation and denoising using robust rank-regularized formulations. The proposed approach is suitable for large scale problems, since it avoids SVD computations by using factorized formulations. We illustrate the advantages of the new approach using a seismic line from Gulf of Suez and 5D synthetic seismic data to obtain high quality results for interpolation and denoising, a key application in exploration geophysics.},
	keywords = {denoising, EAGE, interpolation},
	doi = {10.3997/2214-4609.20130388},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/kumar2013EAGEsind/kumar2013EAGEsind.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2013/kumar2013EAGEsind/kumar2013EAGEsind_pres.pdf},
	author = {Rajiv Kumar and Aleksandr Y. Aravkin and Hassan Mansour and Ben Recht and Felix J. Herrmann}
}
@presentation {kumar2013SINBADhss,
	title = {Seismic data interpolation via low-rank matrix factorization in the hierarchical semi-separable representation},
	year = {2013},
	publisher = {SINBAD},
	abstract = {Recent developments in matrix rank optimization have allowed for new computational approaches in the field of seismic data interpolation. One of the main requirements of exploiting rank-minimization approaches is that the target data set should exhibit a low-rank structure. Seismic frequency slices exhibit low-rank structure at the low-frequencies, but not at the high frequencies. This behavior is due to the increase in oscillations as we move from low to high-frequency slices, even though the energy remains focused around the diagonal. Therefore, interpolation via rank minimization in the high-frequency range requires extended formulations that incorporate low-rank structure. We propose an approach for seismic data interpolation which incorporates the Hierarchical Semi-Separable Structure (HSS) inside rank-regularized least-squares formulations for the missing-trace interpolation problem. The proposed approach is suitable for large scale problems, since it avoids SVD computations and uses a low-rank factorized formulation instead. We illustrate the advantages of the new HSS approach by interpolating a seismic line from the Gulf of Suez and compare the reconstruction with conventional rank minimization.},
	keywords = {Presentation, SINBAD, SINBADSPRING2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Spring/kumar2013SINBADhss/kumar2013SINBADhss.pdf},
	author = {Rajiv Kumar and Hassan Mansour and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@conference {aravkin2013ICASSPssi,
	title = {Sparse seismic imaging using variable projection},
	booktitle = {ICASSP},
	year = {2013},
	month = {05},
	abstract = {We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how this data was generated. For example, a sparse green{\textquoteright}s function may be recovered from seismic experimental data using sparsity optimization when the source signature is known. Unfortunately, in practice this information is often missing, and must be recovered from data along with the signal using deconvolution techniques. In this paper, we present a novel methodology to simulta- neously solve for the sparse signal and auxiliary parameters using a recently proposed variable projection technique. Our main contribution is to combine variable projection with spar- sity promoting optimization, obtaining an efficient algorithm for large-scale sparse deconvolution problems. We demon- strate the algorithm on a seismic imaging example.},
	keywords = {Imaging, Optimization, sparsity, variable projection},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICASSP/2013/aravkin2013ICASSPssi/aravkin2013ICASSPssi.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Ning Tu}
}
@techreport {kumar2013ICMLlr,
	title = {An SVD-free Pareto curve approach to rank minimization},
	number = {TR-EOAS-2013-2},
	year = {2013},
	month = {02},
	institution = {UBC},
	abstract = {Recent SVD-free matrix factorization formulations have enabled rank optimization for extremely large-scale systems (millions of rows and columns). In this paper, we consider rank-regularized formulations that only require a target data-fitting error level, and propose an algorithm for the corresponding problem. We illustrate the advantages of the new approach using the Netflix problem, and use it to obtain high quality results for seismic trace interpolation, a key application in exploration geophysics. We show that factor rank can be easily adjusted as the inversion proceeds, and propose a weighted extension that allows known subspace information to improve the results of matrix completion formulations. Using these methods, we obtain high-quality reconstructions for large scale seismic interpolation problems with real data.},
	keywords = {interpolation, low rank},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2013/kumar2013ICMLlr/kumar2013ICMLlr.pdf},
	author = {Aleksandr Y. Aravkin and Rajiv Kumar and Hassan Mansour and Ben Recht and Felix J. Herrmann}
}
@presentation {kumar2013SINBADwrs,
	title = {Wavefield reconstruction with SVD-free low-rank matrix factorization},
	year = {2013},
	publisher = {SINBAD},
	abstract = {As shown in past, we can leverage the ideas from the field of compressed sensing to cast problems like seismic data interpolation or sequential shot data recovery from simultaneous data, as a compressed sensing problem. In this work we will show how we can borrow the same ideas of compressed sensing and cast these problems as matrix completion problems. Instead of sparsity we will show that we can exploit the low-rank structure of seismic data to solve these problems. One of the impediments in rank-minimization problem is the computation of singular values. We will also show how we can solve the rank minimization problems SVD-free. The practical application is divided into three parts: 1. In case of sequential seismic data acquisition, how jittered subsampling helps to recover the better quality data as compared to random subsampling. 2. How the incorporation of reciprocity principles help to enhance the quality of recovered fully sampled data. 3. How we can recover the sequential source data from simultaneous source data.},
	keywords = {Presentation, SINBAD, SINBADFALL2013, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2013/Fall/kumar2013SINBADwrs/kumar2013SINBADwrs.pdf},
	author = {Rajiv Kumar and Aleksandr Y. Aravkin and Hassan Mansour and Ernie Esser and Felix J. Herrmann}
}
@article {aravkin2012IPNuisance,
	title = {Estimating nuisance parameters in inverse problems},
	journal = {Inverse Problems},
	volume = {28},
	number = {11},
	year = {2012},
	month = {10},
	abstract = {Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is variable projection, where nonlinear least squares problems which are linear in some parameters can be very efficiently optimized. In this paper, we extend the idea of projecting out a subset over the variables to a broad class of maximum likelihood (ML) and maximum a posteriori likelihood (MAP) problems with nuisance parameters, such as variance or degrees of freedom. As a result, we are able to incorporate nuisance parameter estimation into large-scale constrained and unconstrained inverse problem formulations. We apply the approach to a variety of problems, including estimation of unknown variance parameters in the Gaussian model, degree of freedom (d.o.f.) parameter estimation in the context of robust inverse problems, automatic calibration, and optimal experimental design. Using numerical examples, we demonstrate improvement in recovery of primary parameters for several large- scale inverse problems. The proposed approach is compatible with a wide variety of algorithms and formulations, and its implementation requires only minor modifications to existing algorithms.},
	keywords = {full waveform inversion, students t, variance},
	doi = {10.1088/0266-5611/28/11/115016},
	url = {http://arxiv.org/abs/1206.6532},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/InverseProblems/2012/aravkin2012IPNuisance/aravkin2012IPNuisance.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen}
}
@presentation {aravkin2012SINBADenp,
	title = {Estimating nuisance parameters in inverse problems},
	year = {2012},
	publisher = {SINBAD},
	abstract = {Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. In this talk, we present the idea of "projecting out" these variables, and how this idea allows us to design methods for solving a broad class of problems with nuisance parameters, such as variance or degrees of freedom. We then discuss several geophysical applications, including including estimation of unknown variance parameters in the Gaussian model for full waveform inversion, degree of freedom (d.o.f.) parameter estimation in the context of robust imaging problems, and robust source estimation.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/aravkin2012SINBADenp/aravkin2012SINBADenp_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
@techreport {rajiv2012SEGFRM,
	title = {Fast methods for rank minimization with applications to seismic-data interpolation},
	number = {TR-EOAS-2012-3},
	year = {2012},
	month = {04},
	institution = {Department of Earth and Ocean Sciences},
	address = {University of British Columbia, Vancouver},
	abstract = {Rank penalizing techniques are an important direction in seismic inverse problems, since they allow improved recovery by exploiting low-rank structure. A major downside of current state of the art techniques is their reliance on the SVD of seismic data structures, which can be prohibitively expensive. Fortunately, recent work allows us to circumvent this problem by working with matrix factorizations. We review a novel approach to rank penalization, and successfully apply it to the seismic interpolation problem by exploiting the low-rank structure of seismic data in the midpoint-offset domain. Experiments for the recovery of 2D monochromatic data matrices and seismic lines represented as 3D volumes support the feasibility and potential of the new approach.},
	keywords = {Optimization, Rank, Seismic data Interpolation},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2012/rajiv2012SEGFRM/rajiv2012SEGFRM.pdf},
	author = {Rajiv Kumar and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@article {Li11TRfrfwi,
	title = {Fast randomized full-waveform inversion with compressive sensing},
	journal = {Geophysics},
	volume = {77},
	number = {3},
	year = {2012},
	month = {05},
	pages = {A13-A17},
	abstract = {Wave-equation based seismic inversion can be formulated as a nonlinear inverse problem where the medium properties are obtained via minimization of a least- squares misfit functional. The demand for higher resolution models in more geologically complex areas drives the need to develop techniques that explore the special structure of full-waveform inversion to reduce the computational burden and to regularize the inverse problem. We meet these goals by using ideas from compressive sensing and stochastic optimization to design a novel Gauss-Newton method, where the updates are computed from random subsets of the data via curvelet-domain sparsity promotion. Application of this idea to a realistic synthetic shows improved results compared to quasi-Newton methods, which require passes through all data. Two different subset sampling strategies are considered: randomized source encoding, and drawing sequential shots firing at random source locations from marine data with missing near and far offsets. In both cases, we obtain excellent inversion results compared to conventional methods at reduced computational costs.},
	keywords = {Compressive Sensing, FWI, Optimization, SLIM},
	doi = {10.1190/geo2011-0410.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2012/Li11TRfrfwi/Li11TRfrfwi.pdf},
	author = {Xiang Li and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {aravkin2012ICASSPfastseis,
	title = {Fast seismic imaging for marine data},
	booktitle = {ICASSP},
	year = {2012},
	publisher = {ICASSP},
	organization = {ICASSP},
	abstract = {Seismic imaging can be formulated as a linear inverse problem where a medium perturbation is obtained via minimization of a least-squares misfit functional. The demand for higher resolution images in more geophysically complex areas drives the need to develop techniques that handle problems of tremendous size with limited computational resources. While seismic imaging is amenable to dimensionality reduction techniques that collapse the data volume into a smaller set of "super-shots", these techniques break down for complex acquisition geometries such as marine acquisition, where sources and receivers move during acquisition. To meet these challenges, we propose a novel method that combines sparsity-promoting (SP) solvers with random subset selection of sequential shots, yielding a SP algorithm that only ever sees a small portion of the full data, enabling its application to very large-scale problems. Application of this technique yields excellent results for a complicated synthetic, which underscores the robustness of sparsity promotion and its suitability for seismic imaging.},
	keywords = {ICASSP},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICASSP/2012/AravkinLiHerrmann/AravkinLiHerrmann.pdf},
	author = {Aleksandr Y. Aravkin and Xiang Li and Felix J. Herrmann}
}
@presentation {aravkin2012SINBADgsf,
	title = {Generalized SPGL1: from theory to applications},
	year = {2012},
	publisher = {SINBAD},
	abstract = {The SPGL1 solver has been effectively used for many geophysical applications, including curvelet data interpolation, imaging, and as a subroutine in full waveform inversion. In this talk, we present an overview of the theoretical foundation of the solver, along with a broad generalization of this foundation. We then introduce several applications, including robust \& sparse imaging, sparse deconvolution, and data interpolation by matrix completion.},
	keywords = {Presentation, SINBAD, SINBADFALL2012, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2012/Fall/aravkin2012SINBADgsf/aravkin2012SINBADgsf_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
@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}
}
@conference {aravkin2012SEGST,
	title = {On non-uniqueness of the Student{\textquoteright}s t-formulation for linear inverse problems},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {31},
	year = {2012},
	month = {11},
	pages = {1-5},
	publisher = {SEG},
	organization = {SEG},
	abstract = {We review the statistical interpretation of inverse problem formulations, and the motivations for selecting non-convex penalties for robust behaviour with respect to measurement outliers or artifacts in the data. An important downside of using non-convex formulations such as the Student{\textquoteright}s t is the potential for non-uniqueness, and we present a simple example where the Student{\textquoteright}s t penalty can be made to have many local minima by appropriately selecting the degrees of freedom parameter. On the other hand, the non-convexity of the Student{\textquoteright}s t is precisely what gives it the ability to ignore artifacts in the data. We explain this idea, and present a stylized imaging experiment, where the Student{\textquoteright}s t is able to recover a velocity perturbation from data contaminated by a very peculiar artifact {\textendash}- data from a different velocity perturbation. The performance of Student{\textquoteright}s t inversion is investigated empirically for different values of the degrees of freedom parameter, and different initial conditions.},
	keywords = {non-convex, robust, SEG, Student{\textquoteright}s t, uniqueness},
	doi = {10.1190/segam2012-1558.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/aravkin2012SEGST/aravkin2012SEGST.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Kenneth Bube and Felix J. Herrmann}
}
@article {Aravkin11TRridr,
	title = {Robust inversion, dimensionality reduction, and randomized sampling},
	journal = {Mathematical Programming},
	volume = {134},
	number = {1},
	year = {2012},
	month = {08},
	pages = {101-125},
	abstract = {We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only viable, however, for a least-squares misfit, which is sensitive to outliers in the data and artifacts unexplained by the forward model. This motivates us to propose a robust formulation based on the Student{\textquoteright}s t-distribution of the error. We demonstrate how the corresponding penalty function, together with the sampling approach, can obtain good results for a large-scale seismic inverse problem with 50 \% corrupted data.},
	keywords = {FWI, Inverse problems, Optimization, Robust estimation, Seismic inversion, Stochastic optimization},
	doi = {10.1007/s10107-012-0571-6},
	url = {http://www.springerlink.com/content/35rwr101h5736340/},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/MathematicalProgramming/aravkin2012MPrid/aravkin2012MPrid.pdf},
	author = {Aleksandr Y. Aravkin and Michael P. Friedlander and Felix J. Herrmann and Tristan van Leeuwen}
}
@conference {aravkin2012ICASSProbustb,
	title = {Robust inversion via semistochastic dimensionality reduction},
	booktitle = {ICASSP},
	year = {2012},
	pages = {5245-5248},
	publisher = {ICASSP},
	organization = {ICASSP},
	abstract = {We consider a class of inverse problems where it is possible to aggregate the results of multiple experiments. This class includes problems where the forward model is the solution operator to linear ODEs or PDEs. The tremendous size of such problems motivates the use dimensionality reduction (DR) techniques based on randomly mixing experiments. These techniques break down, however, when robust data-fitting formulations are used, which are essential in cases of missing data, unusually large errors, and systematic features in the data unexplained by the forward model. We survey robust methods within a statistical framework, and propose a sampling optimization approach that allows DR. The efficacy of the methods are demonstrated for a large-scale seismic inverse problem using the robust Student{\textquoteright}s t-distribution, where a useful synthetic velocity model is recovered in the extreme scenario of 60\% corrupted data. The sampling approach achieves this recovery using 20\% of the effort required by a direct robust approach.},
	keywords = {ICASSP},
	doi = {10.1109/ICASSP.2012.6289103},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICASSP/2012/AravkinFriedlanderLeeuwen/AravkinFriedlanderLeeuwen.pdf},
	author = {Aleksandr Y. Aravkin and Michael P. Friedlander and Tristan van Leeuwen}
}
@conference {aravkin2012EAGErobust,
	title = {Source estimation for frequency-domain FWI with robust penalties},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2012},
	month = {06},
	abstract = {Source estimation is an essential component of full waveform inversion. In the standard frequency domain formulation, there is closed form solution for the the optimal source weights, which can thus be cheaply estimated on the fly. A growing body of work underscores the importance of robust modeling for data with large outliers or artifacts that are not captured by the forward model. Effectively, the least-squares penalty on the residual is replaced by a robust penalty, such as Huber, Hybrid {\textquoteleft}1-{\textquoteleft}2 or Student{\textquoteright}s t. As we will demonstrate, it is essential to use the same robust penalty for source estimation. In this abstract, we present a general approach to robust waveform inversion with robust source estimation. In this general formulation, there is no closed form solution for the optimal source weights so we need to solve a scalar optimization problem to obtain these weights. We can efficiently solve this optimization problem with a Newton-like method in a few iterations. The computational cost involved is of the same order as the usual least-squares source estimation procedure. We show numerical examples illustrating robust source estimation and robust waveform inversion on synthetic data with outliers.},
	keywords = {EAGE},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/aravkin2012EAGErobust/aravkin2012EAGErobust.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2012/aravkin2012EAGErobust/aravkin2012EAGErobust_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=59196},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Henri Calandra and Felix J. Herrmann}
}
@presentation {aravkin2011SINBADesp,
	title = {Extensions to sparsity promotion},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/aravkin2011SINBADesp/aravkin2011SINBADesp_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
@conference {herrmann2011SEGffw,
	title = {Fast full-waveform inversion with compressive sensing},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2011},
	keywords = {Full-waveform inversion, SEG, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/HerrmannSEG2011fws/HerrmannSEG2011fws.pdf},
	author = {Aleksandr Y. Aravkin and Felix J. Herrmann and Tristan van Leeuwen and Xiang Li}
}
@conference {aravkin2011SIAMfwi,
	title = {Full waveform inversion with compressive updates},
	booktitle = {SIAM},
	year = {2011},
	publisher = {SIAM CS\&E 2011},
	organization = {SIAM CS\&E 2011},
	abstract = {Full-waveform inversion relies on large multi-experiment data volumes. While improvements in acquisition and inversion have been extremely successful, the current push for higher quality models reveals fundamental shortcomings handling increasing problem sizes numerically. To address this fundamental issue, we propose a randomized dimensionality-reduction strategy motivated by recent developments in stochastic optimization and compressive sensing. In this formulation conventional Gauss-Newton iterations are replaced by dimensionality-reduced sparse recovery problems with source encodings.},
	keywords = {Full-waveform inversion, SLIM},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SIAM/2011/aravkin2011SIAMfwi/aravkin2011SIAMfwi.pdf},
	author = {Aleksandr Y. Aravkin and Felix J. Herrmann and Tristan van Leeuwen and James V. Burke and Xiang Li}
}
@conference {herrmann2011SLRAfwi,
	title = {Full waveform inversion with compressive updates},
	booktitle = {SLRA},
	year = {2011},
	publisher = {Sparse and Low Rank Approximation 2011},
	organization = {Sparse and Low Rank Approximation 2011},
	abstract = {Full-waveform inversion relies on large multi-experiment data volumes. While improvements in acquisition and inversion have been extremely successful, the current push for higher quality models reveals fundamental shortcomings handling increasing problem sizes numerically. To address this fundamental issue, we propose a randomized dimensionality-reduction strategy motivated by recent developments in stochastic optimization and compressive sensing. In this formulation conventional Gauss-Newton iterations are replaced by dimensionality-reduced sparse recovery problems with source encodings.},
	keywords = {Full-waveform inversion},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SLRA/2011/herrmann2011SLRAfwi/herrmann2011SLRAfwi.pdf},
	author = {Felix J. Herrmann and Aleksandr Y. Aravkin and Xiang Li and Tristan van Leeuwen}
}
@conference {li2011EAGEfwirr,
	title = {Full-waveform inversion with randomized L1 recovery for the model updates},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2011},
	month = {05},
	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 results. 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 "curse of dimensionality" exemplified by Nyquist{\~O}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 "curse of dimensionality" by randomized dimensionality reduction of the FWI problem adapted from the field of CS. We invert for model updates by replacing the Gauss-Newton linearized subproblem for subsampled FWI with a sparsity promoting formulation, and solve this formulation using the SPGl1 algorithm. We speed up the algorithm and avoid overfitting the data by solving for the linearized updates only approximately. Our approach is successful because it reduces the size of seismic data volumes without loss of information. With this reduction, we can compute a Newton-like update with the reduced data volume at the cost of roughly one gradient update for the fully sampled wavefield.},
	keywords = {EAGE, Full-waveform inversion, Presentation},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/li11EAGEfwirr/li11EAGEfwirr.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/li11EAGEfwirr/li11EAGEfwirr_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=50345},
	author = {Xiang Li and Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@conference {herrmann2011ICIAMconvexcompfwi,
	title = {FWI with sparse recovery: a convex-composite approach},
	booktitle = {ICIAM},
	year = {2011},
	month = {07},
	publisher = {ICIAM 2011},
	organization = {ICIAM 2011},
	abstract = {Iterative inversion algorithms require repeated simulation of 3D time-dependent acoustic, elastic, or electromagnetic wave fields, extending hundreds of wavelengths and hundreds of periods. Also, seismic data is rich in information at every representable scale. Thus simulation-driven optimization approaches to inversion impose great demands on simulator efficiency and accuracy. While computer hardware advances have been of critical importance in bringing inversion closer to practical application, algorithmic advances in simulator methodology have been equally important. Speakers in this two-part session will address a variety of numerical issues arising in the wave simulation, and in its application to inversion.},
	keywords = {Full-waveform inversion, ICIAM, Optimization},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICIAM/2011/herrmann2011ICIAMconvexcompfwi/herrmann2011ICIAMconvexcompfwi.pdf},
	author = {Felix J. Herrmann and Aleksandr Y. Aravkin and Tristan van Leeuwen and Xiang Li}
}
@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 {aravkin2011EAGEnspf,
	title = {A nonlinear sparsity promoting formulation and algorithm for full waveform inversion},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2011},
	month = {05},
	abstract = {Full Waveform Inversion (FWI) is a computational procedure to extract medium parameters from seismic data. FWI is typically formulated as a nonlinear least squares optimization problem, and various regularization techniques are used to guide the optimization because the problem is illposed. In this paper, we propose a novel sparse regularization which exploits the ability of curvelets to efficiently represent geophysical images. We then formulate a corresponding sparsity promoting constrained optimization problem, which we call Nonlinear Basis Pursuit Denoise (NBPDN) and present an algorithm to solve this problem to recover medium parameters. The utility of the NBPDN formulation and efficacy of the algorithm are demonstrated on a stylized cross-well experiment, where a sparse velocity perturbation is recovered with higher quality than the standard FWI formulation (solved with LBFGS). The NBPDN formulation and algorithm can recover the sparse perturbation even when the data volume is compressed to 5 \% of the original size using random superposition.},
	keywords = {EAGE, Full-waveform inversion, Optimization},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/aravkin11EAGEnspf/aravkin11EAGEnspf.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/aravkin11EAGEnspf/aravkin11EAGEnspf_pres.pdf},
	url2 = {http://earthdoc.eage.org/publication/publicationdetails/?publication=50199},
	author = {Aleksandr Y. Aravkin and James V. Burke and Felix J. Herrmann and Tristan van Leeuwen}
}
@presentation {aravkin2011SINBADrsp,
	title = {A randomized, sparsity promoting, Gauss-Newton algorithm for seismic waveform inversion},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/aravkin2011SINBADrsp/aravkin2011SINBADrsp_pres.pdf},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/aravkin2011SINBADrsp/li2011SINBADrsp_pres.pdf},
	author = {Aleksandr Y. Aravkin and Xiang Li}
}
@conference {aravkin2011SEGrobust,
	title = {Robust full-waveform inversion using the Student{\textquoteright}s t-distribution},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {30},
	year = {2011},
	month = {09},
	pages = {2669-2673},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Full-waveform inversion (FWI) is a computational procedure to extract medium parameters from seismic data. Robust methods for FWI are needed to overcome sensitivity to noise and in cases where modeling is particularly poor or far from the real data generating process. We survey previous robust methods from a statistical perspective, and use this perspective to derive a new robust method by assuming the random errors in our model arise from the Student{\textquoteright}s t-distribution. We show that in contrast to previous robust methods, the new method progres- sively down-weighs large outliers, effectively ignoring them once they are large enough. This suggests that the new method is more robust and suitable for situations with very poor data quality or modeling. Experiments show that the new method recovers as well or better than previous robust methods, and can recover models with quality comparable to standard methods on noise-free data when some of the data is completely corrupted, and even when a marine acquisition mask is entirely ignored in the modeling. The ability to ignore a marine acquisition mask via robust FWI methods offers an opportunity for stochastic optimization methods in marine acquisition.},
	keywords = {Full-waveform inversion, Optimization, SEG},
	doi = {10.1190/1.3627747},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/aravkin11SEGrobust/aravkin11SEGrobust.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@presentation {aravkin2011SINBADrfwi,
	title = {Robust FWI using Student{\textquoteright}s t \& robust source estimation},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Fall/aravkin2011SINBADrfwi/aravkin2011SINBADrfwi_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
@presentation {aravkin2011SINBADSPRINGrfwi,
	title = {Robust FWI using Student{\textquoteright}s t-distribution},
	year = {2011},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADSPRING2011, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2011/Spring/aravkin2011SINBADSPRINGrfwi/aravkin2011SINBADSPRINGrfwi_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
@conference {aravkin2011ICIAMrfwiu,
	title = {Robust FWI using Student{\textquoteright}s t-distribution},
	booktitle = {ICIAM},
	year = {2011},
	month = {07},
	publisher = {ICIAM 2011},
	organization = {ICIAM 2011},
	abstract = {Iterative inversion algorithms require repeated simulation of 3D time-dependent acoustic, elastic, or electromagnetic wave fields, extending hundreds of wavelengths and hundreds of periods. Also, seismic data is rich in information at every representable scale. Thus simulation-driven optimization approaches to inversion impose great demands on simulator efficiency and accuracy. While computer hardware advances have been of critical importance in bringing inversion closer to practical application, algorithmic advances in simulator methodology have been equally important. Speakers in this two-part session will address a variety of numerical issues arising in the wave simulation, and in its application to inversion.},
	keywords = {Full-waveform inversion, ICIAM, Optimization, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICIAM/2011/aravkin2011ICIAMrfwiu/aravkin2011ICIAMrfwiu.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and Felix J. Herrmann}
}
@article {vanLeeuwen2010IJGswi,
	title = {Seismic waveform inversion by stochastic optimization},
	journal = {International Journal of Geophysics},
	volume = {2011},
	year = {2011},
	note = {Article ID: 689041, 18pages},
	month = {12},
	abstract = {We explore the use of stochastic optimization methods for seismic waveform inversion. The basic principle of such methods is to randomly draw a batch of realizations of a given misfit function and goes back to the 1950s. The ultimate goal of such an approach is to dramatically reduce the computational cost involved in evaluating the misfit. Following earlier work, we introduce the stochasticity in waveform inversion problem in a rigorous way via a technique called randomized trace estimation. We then review theoretical results that underlie recent developments in the use of stochastic methods for waveform inversion. We present numerical experiments to illustrate the behavior of different types of stochastic optimization methods and investigate the sensitivity to the batch size and the noise level in the data. We find that it is possible to reproduce results that are qualitatively similar to the solution of the full problem with modest batch sizes, even on noisy data. Each iteration of the corresponding stochastic methods requires an order of magnitude fewer PDE solves than a comparable deterministic method applied to the full problem, which may lead to an order of magnitude speedup for waveform inversion in practice.},
	keywords = {FWI, Optimization, SLIM},
	doi = {10.1155/2011/689041},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InternationJournalOfGeophysics/2011/vanLeeuwen10IJGswi/vanLeeuwen10IJGswi.pdf},
	author = {Tristan van Leeuwen and Aleksandr Y. Aravkin and Felix J. Herrmann}
}
@conference {aravkin2011EAGEspfwi,
	title = {Sparsity promoting formulations and algorithms for FWI},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2011},
	keywords = {EAGE, Full-waveform inversion},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2011/Aravkin2011EAGEspfwi/Aravkin2011EAGEspfwi.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and James V. Burke and Felix J. Herrmann}
}
@conference {aravkin2011ICIAMspf,
	title = {Sparsity promoting formulations and algorithms for FWI},
	booktitle = {ICIAM},
	year = {2011},
	note = {Presented at AMP Medical and Seismic Imaging, 2011, Vancouver BC.},
	month = {07},
	publisher = {ICIAM 2011},
	organization = {ICIAM 2011},
	abstract = {Full Waveform Inversion (FWI) is a computational procedure to extract medium parameters from seismic data. FWI is typically formulated as a nonlinear least squares optimization problem, and various regularization techniques are used to guide the optimization because the problem is ill-posed. We propose a novel sparse regularization which exploits the ability of curvelets to efficiently represent geophysical images. We then formulate a corresponding sparsity promoting constrained optimization problem, which we solve using an open source algorithm. The techniques are applicable to any inverse problem where sparsity modeling is appropriate. We demonstrate the efficacy of the formulation on a toy example (stylized cross-well experiment) and on a realistic Seismic example (partial Marmoussi model). We also discuss the tradeoff between model fit and sparsity promotion, with a view to extend existing techniques for linear inverse problems to the case where the forward model is nonlinear.},
	keywords = {Full-waveform inversion, Optimization, Presentation, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ICIAM/2011/aravkin2011ICIAMspf/aravkin2011ICIAMspf_pres.pdf},
	author = {Aleksandr Y. Aravkin and Tristan van Leeuwen and James V. Burke and Felix J. Herrmann}
}
@presentation {aravkin2010SINBADesf,
	title = {Exploiting sparsity in full-waveform inversion: nonlinear basis pursuit denoise algorithm},
	year = {2010},
	publisher = {SINBAD},
	keywords = {Presentation, SINBAD, SINBADFALL2010, SLIM},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SINBAD/2010/Fall/aravkin2010SINBADesf/aravkin2010SINBADesf_pres.pdf},
	author = {Aleksandr Y. Aravkin}
}
@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}
}
