@techreport {witte2017TRcls,
	title = {Compressive least-squares migration with source estimation},
	number = {TR-EOAS-2017-3},
	year = {2017},
	institution = {UBC},
	abstract = {Least-squares reverse-time migration is a powerful approach for true-amplitude seismic imaging of complex geological structures. The successful application of this method is hindered by its exceedingly large computational cost and required prior knowledge of the generally unknown source wavelet. We address these problems by introducing an algorithm for low-cost sparsity-promoting least-squares migration with source estimation. We adapt a recent algorithm from sparse optimization, which allows to work with randomized subsets of shots during each iteration of least-squares migration, while still converging to an artifact-free solution. We modify the algorithm to incorporate on-the-fly source estimation through variable projection, which lets us estimate the wavelet without additional PDE solves. The algorithm is easy to implement and allows imaging at a fraction of the cost of conventional least squares reverse-time migration, requiring only around two passes trough the data, making the method feasible for large-scale imaging problems with unknown source wavelets.},
	keywords = {LSRTM, migration, source estimation, sparsity, time domain},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2017/witte2017TRcls/witte2017TRcls.html},
	author = {Philipp A. Witte and Mengmeng Yang and Felix J. Herrmann}
}
@conference {yang2017SEGfsp,
	title = {Fast sparsity-promoting least-squares migration with multiples in time domain},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2017},
	note = {(SEG, Houston)},
	month = {09},
	pages = {4828-4832},
	abstract = {Based on the latest developments of research in inversion technology with optimization, researchers have made significant progress in the implementation of least-squares reverse-time migration (LS-RTM) of primaries. In Marine data however, these applications rely on the success of a pre-imaging separation of primaries and multiples, which can be modeled as a multi-dimensional convolution between the vertical derivative of the surface-free Green{\textquoteright}s function and the down-going receiver wavefield. Instead of imaging the primaries and multiples separately, we implement the LS-RTM of the total down-going wavefield by combining areal source injection and linearized Born modelling, where strong surface related multiples are generated from a strong density variation at the ocean bottom. The advantage including surface related multiples in LS-RTM is the extra illumination we obtain from these multiples without incurring additional computational costs related to carrying out multi-dimensional convolutions part of conventional multiple prediction procedures. Even though we are able to avert these computational costs, our approach shares the large costs of LSRTM. We reduce these costs by combining randomized source subsampling with our sparsity-promoting imaging technology, which produces artifact-free, high-resolution images, with the surface-related multiples migrated properly.},
	keywords = {least-squares RTM, multiples, SEG, sparsity, time domain},
	doi = {10.1190/segam2017-17741608.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/yang2017SEGfsp/yang2017SEGfsp.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2017/yang2017SEGfsp/yang2017SEGfsp_pres.pdf},
	author = {Mengmeng Yang and Emmanouil Daskalakis and Felix J. Herrmann}
}
@article {lin2015scatterEPSI,
	title = {Estimation of primaries by sparse inversion with scattering-based multiple predictions for data with large gaps},
	journal = {Geophysics},
	volume = {81},
	number = {3},
	year = {2016},
	note = {(Geophysics)},
	month = {05},
	pages = {V183-V197},
	abstract = {We propose to solve the Estimation of Primaries by Sparse Inversion problem without any explicit data reconstruction, from a seismic record with missing near-offsets and large holes in the acquisition grid which does not produce aliasing but otherwise causes large errors in the multiple prediction. Exclusion of the unknown data as an inversion variable from the process is desirable, since it sidesteps possible issues arising from fitting observations that are also unknowns in the same inversion problem. Instead, we simulate their multiple contributions by augmenting the forward prediction model for the total wavefield with a scattering series that mimics the action of the free surface reflector within the confines of the unobserved trace locations. Each term in this scattering series simply involves convolution of the predicted wavefield once more with the current estimated surface-free Green{\textquoteright}s function at these unobserved locations. We investigate the necessary modifications to the primary estimation algorithm to account for the resulting nonlinearity in the modeling operator, and also demonstrate that just a few scattering terms are enough to satisfactorily mitigate the effects of near-offset data gaps during the inversion process. Numerical experiments on synthetic data show that the final derived method can significantly outperform explicit data reconstruction for large near-offset gaps. This is achieved with a similar computational cost and better memory efficiency compared to explicit data reconstruction. We also show on real data that our scheme outperforms pre-interpolation of the near-offset gap.},
	keywords = {EPSI, multiples, Optimization, REPSI, scattering, sparsity},
	doi = {10.1190/geo2015-0263.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2016/lin2015scatterEPSI/lin2015scatterEPSI.html},
	author = {Tim T.Y. Lin and Felix J. Herrmann}
}
@mastersthesis {lin2015THpes,
	title = {Primary estimation with sparsity-promoting bi-convex optimization},
	year = {2015},
	note = {(PhD)},
	month = {10},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {This thesis establishes a novel inversion methodology for the surface-related primaries from a given recorded seismic wavefield, called the Robust Estimation of Primaries by Sparse Inversion (Robust EPSI, or REPSI). Surface-related multiples are a major source of coherent noise in seismic data, and inferring fine geological structures from active-source seismic recordings typically first necessitates its removal or mitigation. For this task, current practice calls for data-driven approaches which produce only approximate multiple models that must be non-linearly subtracted from the data, often distorting weak primary events in the process. A recently proposed method called Estimation of Primaries by Sparse Inversion (EPSI) avoids this adaptive subtraction by directly inverting for a discrete representation of the underlying multiple-free subsurface impulse response as a set of band-limited spikes. However, in its original form, the EPSI algorithm exhibits a few notable shortcomings that impede adoption. Although it was shown that the correct impulse response can be obtained through a sparsest solution criteria, the current EPSI algorithm is not designed to take advantage of this finding, but instead approximates a sparse solution in an ad-hoc manner that requires practitioners to decide on a multitude of inversion parameters. The Robust EPSI method introduced in this thesis reformulates the original EPSI problem as a formal bi-convex optimization problem that makes obtaining the sparsest solution an explicit goal, while also reliably admit satisfactory solutions using contemporary self-tuning gradient methods commonly seen in large-scale machine learning communities. I show that the Robust EPSI algorithm is able to operate successfully on a variety of datasets with minimal user input, while also producing a more accurate model of the subsurface impulse response when compared to the original algorithm. Furthermore, this thesis makes several contributions that improves the capability and practicality of EPSI: a novel scattering-based multiple prediction model that allows Robust EPSI to deal with wider near-offset receiver gaps than previously demonstrated for EPSI, as well as a multigrid-inspired continuation strategy that significantly reduces the computation time needed to solve EPSI-type problems. These additions are enabled by and built upon the formalism of the Robust EPSI as developed in this thesis.},
	keywords = {biconvex, EPSI, inversion, multiples, Optimization, PhD, sparsity},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2015/lin2015THpes/lin2015THpes.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2015/lin2015THpes/lin2015THpes_pres.pdf},
	author = {Tim T.Y. Lin}
}
@article {kumar2015sss,
	title = {Source separation for simultaneous towed-streamer marine acquisition {\textendash}- a compressed sensing approach},
	journal = {Geophysics},
	volume = {80},
	number = {6},
	year = {2015},
	note = {(Geophysics)},
	month = {11},
	pages = {WD73-WD88},
	abstract = {Simultaneous marine acquisition is an economic way to sample seismic data and speed up acquisition, wherein single or multiple source vessels fire sources at near-simultaneous or slightly random times, resulting in overlapping shot records. The current paradigm for simultaneous towed-streamer marine acquisition incorporates {\textquotedblleft}low variability{\textquotedblright} in source firing times, i.e., 0 <= 1 or 2 s because the sources and receivers are moving. This results in a low degree of randomness in simultaneous data, which is challenging to separate (into its constituent sources) using compressed-sensing-based separation techniques because randomization is key to successful recovery via compressed sensing. We have addressed the challenge of source separation for simultaneous towed-streamer acquisitions via two compressed-sensing-based approaches, i.e., sparsity promotion and rank minimization. We have evaluated the performance of the sparsity-promotion- and rank-minimization-based techniques by simulating two simultaneous towed-streamer acquisition scenarios, i.e., over/under and simultaneous long offset. A field data example from the Gulf of Suez for the over/under acquisition scenario was also developed. We observed that the proposed approaches gave good and comparable recovery qualities of the separated sources, but the rank-minimization technique outperformed the sparsity-promoting technique in terms of the computational time and memory. We also compared these two techniques with the normal-moveout-based median-filtering-type approach, which had comparable results.},
	keywords = {2D, Acquisition, inversion, marine, Optimization, Rank, source separation, sparsity},
	doi = {10.1190/geo2015-0108.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2015/kumar2015sss/kumar2015sss_revised.pdf},
	url2 = {http://library.seg.org/doi/abs/10.1190/geo2015-0108.1},
	author = {Rajiv Kumar and Haneet Wason and Felix J. Herrmann}
}
@conference {tu2013SEGcle,
	title = {Controlling linearization errors in $\ell_1$ regularized inversion by rerandomization},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {32},
	year = {2013},
	month = {09},
	pages = {4640-4644},
	abstract = {Linearized inversion is a data fitting procedure that tries to match the observed seismic data with data predicted by linearized modelling. In practice, the observed data is not necessarily in the column space of the linearized modelling operator. This can be caused by lack of an accurate background velocity model or by coherent noises not explained by linearized modelling. Through carefully designed experiments, we ob- serve that a moderate data mismatch does not pose an issue if we can use all the data in the inversion. However, artifacts do arise from the mismatch when randomized dimensionality reduction techniques are adopted to speed up the inversion. To stabilize the inversion for dimensionality reduction with randomized source aggregates, we propose to rerandomize by drawing independent simultaneous sources occasionally during the inversion. The effect of this rerandomization is remarkable because it results in virtually artifact-free images at a cost comparable to a single reverse-time migration. Implications of our method are profound because we are now able to resolve fine-scale steep subsalt features in a computationally feasible manner.},
	keywords = {inversion, message passing, rerandomization, SEG, sparsity},
	doi = {10.1190/segam2013-1302.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/tu2013SEGcle/tu2013SEGcle.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2013/tu2013SEGcle/tu2013SEGcle_pres.pdf},
	author = {Ning Tu and Xiang Li and Felix J. Herrmann}
}
@article {lin2013GEOPrepsi,
	title = {Robust estimation of primaries by sparse inversion via one-norm minimization},
	journal = {Geophysics},
	volume = {78},
	number = {3},
	year = {2013},
	month = {05},
	pages = {R133-R150},
	abstract = {A recently proposed method called estimation of primaries by sparse inversion (EPSI) avoids the need for adaptive subtraction of approximate multiple predictions by directly inverting for the multiple-free subsurface impulse response as a collection of band-limited spikes. Although it can be shown that the correct primary impulse response is obtained through the sparsest possible solution, the original EPSI algorithm was not designed to take advantage of this result, and instead it relies on a multitude of inversion parameters, such as the level of sparsity per gradient update. We proposed and tested a new algorithm, named robust EPSI, in which we make obtaining the sparsest solution an explicit goal. Our approach remains a gradient-based approach like the original algorithm, but it is derived from a new biconvex optimization framework based on an extended basis-pursuit denoising formulation. Furthermore, because it is based on a general framework, robust EPSI can recover the impulse response in transform domains, such as sparsifying curvelet-based representations, without changing the underlying algorithm. We discovered that the sparsity-minimizing objective of our formulation enabled it to operate successfully on a variety of synthetic and field marine data sets without excessive tweaking of inversion parameters. We also found that recovering the solution in alternate sparsity domains can significantly improve the quality of the directly estimated primaries, especially for weaker late-arrival events. In addition, we found that robust EPSI produces a more artifact-free impulse response compared to the original algorithm.},
	keywords = {algorithm, biconvex, EPSI, multiples, Optimization, Pareto, sparsity, waveform inversion},
	doi = {10.1190/geo2012-0097.1},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2013/lin2013GEOPrepsi/lin2013GEOPrepsi.pdf},
	author = {Tim T.Y. Lin 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}
}
