@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 {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}
}
@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}
}
@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}
}
@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}
}
@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}
}
@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}
}
@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}
}
