@article {lopez2020gsb,
	title = {Spectral Gap-Based Seismic Survey Design},
	journal = {IEEE Transactions on Geoscience and Remote Sensing},
	year = {2023},
	month = {1},
	abstract = {Seismic imaging in challenging sedimentary basins and reservoirs requires acquiring, processing, and imaging very large volumes of data (tens of terabytes). To reduce the cost of acquisition and the time from acquiring the data to producing a subsurface image, novel acquisition systems based on compressive sensing, low-rank matrix recovery, and randomized sampling have been developed and implemented. These approaches allow practitioners to achieve dense wavefield reconstruction from a substantially reduced number of field samples. However, designing acquisition surveys suited for this new sampling paradigm remains a critical and challenging role in oil, gas, and geothermal exploration. Typical random designs studied in the low-rank matrix recovery and compressive sensing literature are difficult to achieve by standard industry hardware. For practical purposes, a compromise between stochastic and realizable samples is needed. In this paper, we propose a deterministic and computationally cheap tool to alleviate randomized acquisition design, prior to survey deployment and large-scale optimization. We consider universal and deterministic matrix completion results in the context of seismology, where a bipartite graph representation of the source-receiver layout allows for the respective spectral gap to act as a quality metric for wavefield reconstruction. We provide realistic scenarios to demonstrate the utility of the spectral gap as a flexible tool that can be incorporated into existing survey design workflows for successful seismic data acquisition via low-rank and sparse signal recovery.},
	keywords = {biadjacency matrix, bipartite graph, Compressive Sensing, IEEE, low rank matrix completion, nuclear norm minimization, seismic data, seismic trace interpolation, spectral gap},
	doi = {10.1109/TGRS.2023.3237464},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETGRS/2023/lopez2020gsb/lopez2020gsb.pdf},
	author = {Oscar Lopez and Rajiv Kumar and Nick Moldoveanu and Felix J. Herrmann}
}
@conference {yin2021SEGcts,
	title = {Compressive time-lapse seismic monitoring of carbon storage and sequestration with the joint recovery model},
	booktitle = {SEG Technical Program Expanded Abstracts},
	year = {2021},
	note = {(IMAGE, Denver)},
	month = {09},
	pages = {3434-3438},
	abstract = {Time-lapse seismic monitoring of carbon storage and sequestration is often challenging because the time-lapse signature of the growth of CO$_2$ plumes is weak in amplitude and therefore difficult to detect seismically. This situation is compounded by the fact that the surveys are often coarsely sampled and not replicated to reduce costs. As a result, images obtained for different vintages (baseline and monitor surveys) often contain artifacts that may be attributed wrongly to time-lapse changes. To address these issues, we propose to invert the baseline and monitor surveys jointly. By using the joint recovery model, we exploit information shared between multiple time-lapse surveys. Contrary to other time-lapse methods, our approach does not rely on replicating the surveys to detect time-lapse changes. To illustrate this advantage, we present a numerical sensitivity study where CO$_2$ is injected in a realistic synthetic model. This model is representative of the geology in the southeast of the North Sea, an area currently considered for carbon sequestration. Our example demonstrates that the joint recovery model improves the quality of time-lapse images allowing us to monitor the CO$_2$ plume seismically.},
	keywords = {CCS, Compressive Sensing, Imaging, JRM, marine, SEG, time-lapse},
	doi = {10.1190/segam2021-3569087.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/yin2021SEGcts/yin2021SEGcts.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/yin2021SEGcts/Tue-9-28-Yin.html},
	url2 = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2021/yin2021SEGcts/yin2021SEGcts.mp4},
	software = {https://github.com/slimgroup/Software.SEG2021},
	author = {Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {yin2021ML4SEISMICism,
	title = {Improved seismic monitoring of CO2 sequestration with the weighted joint recovery model},
	year = {2021},
	month = {11},
	abstract = {Time-lapse seismic monitoring of CO2 sequestration is challenging because the time-lapse signature of CO2 plumes is weak in amplitude and often contaminated by imaging artifacts due to coarsely sampled, noisy, and non-replicated surveys. In this talk, we present a sparsity-promoting least-squares imaging method where the baseline, and the current and past monitor surveys are inverted jointly. We demonstrate that the sensitivity of seismic monitoring can be improved by inverting for the common component{\textemdash}i.e., the component shared by all vintages, and innovations with respect to this common component. Combining this joint approach with weighted l1,2-norm minimization leads to a monitoring scheme capable of detecting irregular CO2-plume growth in a realistic geological setting.},
	keywords = {CCS, Compressive Sensing, Imaging, JRM, ML4SEISMIC, SLIM, time-lapse},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/yin2021ML4SEISMICism/Tue-11-20-Yin.html},
	author = {Ziyi Yin and Mathias Louboutin and Felix J. Herrmann}
}
@presentation {zhang2021ML4SEISMICiss,
	title = {Improved seismic survey design by maximizing the spectral gap with global optimization},
	year = {2021},
	month = {11},
	abstract = {Random subsampling is increasingly being used in the acquisition of seismic data to shorten the acquisition time and to reduce costs. However, the design of optimal acquisition geometries is still an ongoing area of research. Matrix completion (MC) is a computationally efficient method to reconstruct fully sampled wavefields from sparsely sampled seismic data. In MC theory, the spectral gap (SG), which is a measure of the connectedness of the graph in expander graph theory, has been used to predict, and to some degree quantify, the quality of wavefield reconstruction, given a specific subsampling scheme (acquisition mask). Building on these insights, we propose an optimization scheme, based on simulated annealing, which finds subsampling masks with large SGs that improve the quality of wavefield reconstruction with MC. The experimental results show that the proposed method successfully increases the SG of the subsampling mask starting from randomly initialized masks. Increasing the SG leads to improved connectivity between the sources and receivers and therefore of the wavefield reconstruction. Numerical experiments confirm a direct relationship between increased SG and improved reconstruction quality. This confirms the value SG analysis brings to the design of seismic surveys without the need to carry out expensive wavefield reconstructions to optimize the acquisition design.},
	keywords = {Acquisition, Compressive Sensing, ML4SEISMIC, SLIM, survey design, wavefield reconstruction},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/ML4SEISMIC/2021/zhang2021ML4SEISMICiss/Tue-10-30-Zhang.pdf},
	author = {Yijun Zhang and Felix J. Herrmann}
}
@presentation {Herrmann2019SEGDL,
	title = {Sometimes it pays to be cheap {\textendash} Compressive time-lapse seismic data acquisition},
	year = {2019},
	note = {(SEG Distinguished Lecture)},
	publisher = {Society of Exploration Geophysicists},
	abstract = {During these times of sustained low oil prices, it is essential to look for new innovative ways to collect (time-lapse) seismic data at reduced costs and preferably also at reduced environmental impact. By now, there is an increasing body of corroborating evidence {\textemdash} whether these are simulated case studies or actual acquisitions on land and marine {\textemdash} that seismic acquisition based on the principles of compressive sensing delivers on this premise by removing the need to acquire replicated dense surveys. Up to ten-fold increases in acquisition efficiency have been reported by industry while there are indications that this breakthrough is only the beginning of a paradigm shift where full-azimuth time-lapse processing will become a reality. To familiarize the audience with this new technology, I will first describe the basics of compressive sensing, how it relates to missing-trace interpolation and simultaneous source acquisition, followed by how this technology is driving innovations in full-azimuth (time-lapse) acquisition, yielding high-fidelity data with a high degree of repeatability and at a fraction of the costs.},
	keywords = {Compressive Sensing, Presentation, Time-lapse Marine Acquisition},
	url = {https://slim.gatech.edu/Publications/Public/Lectures/SEG-DL/2019/Herrmann2019SEGDL/Herrmann2019SEGDL/},
	url2 = {https://slim.gatech.edu/Publications/Public/Lectures/SEG-DL/2019/Herrmann2019SEGDL/Herrmann2019SEGDL.pdf},
	author = {Felix J. Herrmann}
}
@mastersthesis {oghenekohwo2017THetl,
	title = {Economic time-lapse seismic acquisition and imaging{\textendash}-Reaping the benefits of randomized sampling with distributed compressive sensing},
	year = {2017},
	note = {(PhD)},
	month = {08},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {This thesis presents a novel viewpoint on the implicit opportunities randomized surveys bring to time-lapse seismic - which is a proven surveillance tool for hydrocarbon reservoir monitoring. Time-lapse (4D) seismic combines acquisition and processing of at least two seismic datasets (or vintages) in order to extract information related to changes in a reservoir within a specified time interval. The current paradigm places stringent requirements on replicating the 4D surveys, which is an expensive task often requiring uneconomical dense sampling of seismic wavefields. To mitigate the challenges of dense sampling, several advances in seismic acquisition have been made in recent years including the use of multiple sources firing at near simultaneous random times, and the adaptation of Compressive Sensing (CS) principles to design practical acquisition engines that improve sampling efficiency for seismic data acquisition. However, little is known regarding the implications of these developments for time-lapse studies. By conducting multiple experiments modelling surveys adhering to the principles of CS for 4D seismic, I propose a model that demonstrates the feasibility of randomized acquisitions for time-lapse seismic. The proposed joint recovery model (JRM), which derives from distributed CS, exploits the common information in time-lapse data during recovery of dense wavefields from measured subsampled data, providing highly repeatable and high-fidelity vintages. I show that we obtain better vintages when randomized surveys are not replicated, in contrast to standard practice, paving the way for an opportunity to relax the rigorous requirement to replicate surveys precisely. We assert that the vintages obtained using our proposed model are of sufficient quality to serve as inputs to processes that extract time-lapse attributes from which subsurface changes are deduced. Additionally, I show that recovery with the JRM is robust with respect to errors due to differences between actual and recorded postplot information. Finally, I present an opportunity to adapt our model to problems related to time-lapse seismic imaging where the main finding is that we can better delineate time-lapse changes by adapting the joint recovery model to wave-equation based inversion methods.},
	keywords = {Acquisition, Compressive Sensing, distributed compressive sensing, joint recovery, PhD, thesis, time lapse},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2017/oghenekohwo2017THetl/oghenekohwo2017THetl.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2017/oghenekohwo2017THetl/oghenekohwo2017THetl_pres.pdf},
	author = {Felix Oghenekohwo}
}
@conference {oghenekohwo2017EAGEitl,
	title = {Improved time-lapse data repeatability with randomized sampling and distributed compressive sensing},
	booktitle = {EAGE Annual Conference Proceedings},
	year = {2017},
	note = {(EAGE, Paris)},
	month = {06},
	abstract = {Recently, new ideas on randomized sampling for time-lapse seismic acquisition have been proposed to address some of the challenges of replicating time-lapse surveys. These ideas, which stem from distributed compressed sensing (DCS) led to the birth of a joint recovery model (JRM) for processing time-lapse data (noise-free) acquired from non-replicated acquisition geometries. However, when the earth does not change{\textendash}-i.e. no time-lapse{\textemdash}the recovered vintages from two non-replicated surveys should show high repeatability measured in terms of normalized RMS, which is a standard metric for quantifying time-lapse data repeatability. Under this assumption of no time-lapse change, we demonstrate improved repeatability (with JRM) of the recovered data from non-replicated random samplings, first with noisy data and secondly in situations where there are calibration errors i.e. where the acquisition parameters such as source/receiver coordinates are not precise.},
	keywords = {calibration, Compressive Sensing, EAGE, noise, repeatability, time lapse},
	doi = {10.3997/2214-4609.201701389},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2017/oghenekohwo2017EAGEitl/oghenekohwo2017EAGEitl.html},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/EAGE/2017/oghenekohwo2017EAGEitl/oghenekohwo2017EAGEitl_poster.pdf},
	author = {Felix Oghenekohwo and Felix J. Herrmann}
}
@mastersthesis {wason2017THsss,
	title = {Simultaneous-source seismic data acquisition and processing with compressive sensing},
	year = {2017},
	note = {(PhD)},
	month = {08},
	school = {The University of British Columbia},
	type = {phd},
	address = {Vancouver},
	abstract = {The work in this thesis adapts ideas from the field of compressive sensing (CS) that lead to new insights into acquiring and processing seismic data, where we can fundamentally rethink how we design seismic acquisition surveys and process acquired data to minimize acquisition- and processing-related costs. Current efforts towards dense source/receiver sampling and full azimuthal coverage to produce high-resolution images of the subsurface have led to the deployment of multiple sources across survey areas. A step ahead from multisource acquisition is simultaneous-source acquisition, where multiple sources fire shots at near-simultaneous/random times resulting in overlapping shot records, in comparison to no overlaps during conventional sequential-source acquisition. Adoption of simultaneous-source techniques has helped to improve survey efficiency and data density. The engine that drives simultaneous-source technology is simultaneous-source separation {\textendash}- a methodology that aims to recover conventional sequential-source data from simultaneous-source data. This is essential because many seismic processing techniques rely on dense and periodic (or regular) source/receiver sampling. We address the challenge of source separation through a combination of tailored simultaneous-source acquisition design and sparsity-promoting recovery via convex optimization using l1 objectives. We use CS metrics to investigate the relationship between marine simultaneous-source acquisition design and data reconstruction fidelity, and consequently assert the importance of randomness in the acquisition system in combination with an appropriate choice for a sparsifying transform (i.e., curvelet transform) in the reconstruction algorithm. We also address the challenge of minimizing the cost of expensive, dense, periodically-sampled and replicated time-lapse surveying and data processing by adapting ideas from distributed compressive sensing. We show that compressive randomized time-lapse surveys need not be replicated to attain acceptable levels of data repeatability, as long as we know the shot positions (post acquisition) to a sufficient degree of accuracy. We conclude by comparing sparsity-promoting and rank-minimization recovery techniques for marine simultaneous-source separation, and demonstrate that recoveries are comparable; however, the latter approach readily scales to large-scale seismic data and is computationally faster.},
	keywords = {Acquisition, Compressive Sensing, marine, Optimization, PhD, simultaneous source, source separation},
	url = {https://slim.gatech.edu/Publications/Public/Thesis/2017/wason2017THsss/wason2017THsss.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Thesis/2017/wason2017THsss/wason2017THsss_pres.pdf},
	author = {Haneet Wason}
}
@article {tu2014fis,
	title = {Fast imaging with surface-related multiples by sparse inversion},
	journal = {Geophysical Journal International},
	volume = {201},
	number = {1},
	year = {2015},
	note = {(Geophysical Journal International)},
	month = {04},
	pages = {304-317},
	abstract = {In marine exploration seismology, surface-related multiples are usually treated as noise mainly because subsequent processing steps, such as migration velocity analysis and imaging, require multiple-free data. Failure to remove these wavefield components from the data may lead to erroneous estimates for migration velocity or result in strong coherent artefacts that interfere with the imaged reflectors. However, multiples can carry complementary information compared to primaries, as they interact with the free surface and are therefore exposed more to the subsurface. Recent work has shown that when processed correctly multiples can improve seismic illumination. Given a sufficiently accurate background velocity model and an estimate for the source signature, we propose a new and computationally efficient linearized inversion procedure based on two-way wave equations, which produces accurate images of the subsurface from the total upgoing wavefield including surface-related multiples. Modelling of the surface-related multiples in the proposed method derives from the well-known surface-related multiple elimination method. We incur a minimal overhead from incorporating the multiples by having the wave-equation solver carry out the multiple predictions via the inclusion of an areal source instead of expensive dense matrix-matrix multiplications. By using subsampling techniques, we obtain high-quality true-amplitude least-squares migrated images at computational costs of roughly a single reverse-time migration (RTM) with all the data. These images are virtually free of coherent artefacts from multiples. Proper inversion of the multiples would be computationally infeasible without using these techniques that significantly bring down the cost. By promoting sparsity in the curvelet domain and using rerandomization, out method gains improved robustness to errors in the background velocity model, and errors incurred in the linearization of the wave equation with respect to the model. We demonstrate the superior performance of the proposed method compared to the conventional RTM using realistic synthetic examples.},
	keywords = {approximate message passing, Compressive Sensing, curvelet, inversion, Kaczmarz, multiples},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalJournalInternational/2014/tu2014fis/tu2014fis.pdf},
	url2 = {http://gji.oxfordjournals.org/cgi/content/full/ggv020?ijkey=pKzrSXbtxjlOjzd\&keytype=ref},
	author = {Ning Tu and Felix J. Herrmann}
}
@techreport {tschannen2014tdl,
	title = {Time domain least squares migration and dimensionality reduction},
	number = {TR-EOAS-2014-9},
	year = {2014},
	month = {06},
	institution = {UBC},
	abstract = {Least-squares seismic migration (LSM) is a wave equation based linearized inversion problem relying on the minimization of a least-squares misfit function, with respect to the medium perturbation, between recorded and modeled wavefields. Today{\textquoteright}s challenges in Hydrocarbon ex- ploration are to build high resolution images of more and more complicated geological reservoirs, which requires to handle very large systems of equations. The extreme size of the problem com- bined with the fact that it is ill-conditioned make LSM not yet feasible for industrial purposes. To overcome this "curse of dimensionality", dimension reduction and divide-and-conquer tech- niques that aim to decrease the computation time and the required memory, while conserving the image quality, have recently been developed. By borrowing ideas from stochastic optimiza- tion and compressive sensing, the imaging problem is reformulated as an L1-regularized, sparsity promoted LSM. The idea is to take advantage of the compressibility of the model perturbation in the curvelet domain and to work on series of smaller subproblems each involving a small ran- domized subset of data. We try two different subset sampling strategies, artificial randomized simultaneous sources experiments ("supershots") and drawing sequential shots firing at random source locations. These subsets are changed after each subproblem is solved. In both cases we obtain good migration results at significantly reduced computational cost. Application of these methods to a complicated synthetic model yields to encouraging results, underlining the usefulness of sparsity promotion and randomization in time stepping formulation.},
	keywords = {Compressive Sensing, sparsity promotion, Stochastic optimization, Wave equation migration},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2014/tschannen2014tdl/tschannen2014tdl.pdf},
	author = {Valentin Tschannen and Zhilong Fang and Felix J. Herrmann}
}
@article {herrmann2012IIsi,
	title = {Seismic advances},
	journal = {International Innovation},
	year = {2013},
	month = {01},
	pages = {46-49},
	abstract = {Current seismic exploration techniques are hampered by bottlenecks in data sampling and processing due to challenges in data collection, demand for more data and the increasing need to study highly complex geological settings. Professor Felix J. Herrmann{\textquoteright}s group is developing novel techniques to overcome these barriers which could greatly benefit the hydrocarbon industry.},
	keywords = {Compressive Sensing, dynamic nonlinear optimization, seismic exploration techniques, wave-equation-based data mining},
	url = {https://slim.gatech.edu/Publications/Public/Journals/InternationalInnovation/2012/herrmann2012IIsi/herrmann2012IIsi.pdf},
	author = {Felix J. Herrmann}
}
@conference {herrmann2012SEGals,
	title = {Accelerated large-scale inversion with message passing},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {31},
	year = {2012},
	month = {11},
	pages = {1-6},
	publisher = {SEG},
	organization = {SEG},
	abstract = {To meet current-day challenges, exploration seismology increasingly relies on more and more sophisticated algorithms that require multiple paths through all data. This requirement leads to problems because the size of seismic data volumes is increasing exponentially, exposing bottlenecks in IO and computational capability. To overcome these bottlenecks, we follow recent trends in machine learning and compressive sensing by proposing a sparsity-promoting inversion technique that works on small randomized subsets of data only. We boost the performance of this algorithm significantly by modifying a state-of-the-art l1-norm solver to benefit from message passing, which breaks the build up of correlations between model iterates and the randomized linear forward model. We demonstrate the performance of this algorithm on a toy sparse-recovery problem and on a realistic reverse-time-migration example with random source encoding. The improvements in speed, memory use, and output quality are truly remarkable.},
	keywords = {Compressive Sensing, Imaging, Optimization, SEG},
	doi = {10.1190/segam2012-0847.1},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/herrmann2012SEGals/herrmann2012SEGals.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2012/herrmann2012SEGals/herrmann2012SEGals_pres.pdf},
	author = {Felix J. Herrmann}
}
@conference {herrmann2012SSPamp,
	title = {Approximate message passing meets exploration seismology},
	booktitle = {2012 IEEE Statistical Signal Processing Workshop (SSP) (SSP{\textquoteright}12)},
	year = {2012},
	month = {03},
	publisher = {IEEE},
	organization = {IEEE},
	address = {Ann Arbor, Michigan, USA},
	abstract = {Data collection, data processing, and imaging in exploration seismology increasingly hinge on large-scale sparsity promoting solvers to remove artifacts caused by efforts to reduce costs. We show how the inclusion of a {\textquoteright}message term{\textquoteright} in the calculation of the residuals improves the convergence of these iterative solvers by breaking correlations that develop between the model iterate and the linear system that needs to be inverted. We compare this message-passing scheme to state-of-the-art solvers for problems in missing-trace interpolation and in dimensionality-reduced imaging with phase en- coding.},
	keywords = {Compressive Sensing, Exploration seismology, seismic imaging, transform-domain sparsity promotion},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SSP/2012/herrmann2012SSPamp/herrmann2012SSPamp.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SSP/2012/herrmann2012SSPamp/herrmann2012SSPamp_pres.pdf},
	author = {Felix J. Herrmann}
}
@article {herrmann11GPelsqIm,
	title = {Efficient least-squares imaging with sparsity promotion and compressive sensing},
	journal = {Geophysical Prospecting},
	volume = {60},
	number = {4},
	year = {2012},
	month = {07},
	pages = {696-712},
	address = {University of British Columbia, Vancouver},
	abstract = {Seismic imaging is a linearized inversion problem relying on the minimization of a least-squares misfit functional as a function of the medium perturbation. The success of this procedure hinges on our ability to handle large systems of equations{\textendash}-whose size grows exponentially with the demand for higher resolution images in more and more complicated areas{\textendash}-and our ability to invert these systems given a limited amount of computational resources. To overcome this "curse of dimensionality" in problem size and computational complexity, we propose a combination of randomized dimensionality-reduction and divide-and-conquer techniques. This approach allows us to take advantage of sophisticated sparsity-promoting solvers that work on a series of smaller subproblems each involving a small randomized subset of data. These subsets correspond to artificial simultaneous-source experiments made of random superpositions of sequential-source experiments. By changing these subsets after each subproblem is solved, we are able to attain an inversion quality that is competitive while requiring fewer computational, and possibly, fewer acquisition resources. Application of this concept to a controlled series of experiments showed the validity of our approach and the relationship between its efficiency{\textendash}-by reducing the number of sources and hence the number of wave-equation solves{\textendash}-and the image quality. Application of our dimensionality-reduction methodology with sparsity promotion to a complicated synthetic with well-log constrained structure also yields excellent results underlining the importance of sparsity promotion.},
	keywords = {Compressive Sensing, Imaging, Optimization, SLIM},
	doi = {10.1111/j.1365-2478.2011.01041.x},
	url = {https://slim.gatech.edu/Publications/Public/Journals/GeophysicalProspecting/2012/herrmann11GPelsqIm/herrmann11GPelsqIm.pdf},
	url2 = {http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2478.2011.01041.x/full},
	author = {Felix J. Herrmann and Xiang Li}
}
@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}
}
@article {mansour2012IEEETITrcs,
	title = {Recovering compressively sampled signals using partial support information},
	journal = {IEEE Transactions on Information Theory},
	volume = {58},
	number = {2},
	year = {2012},
	month = {02},
	pages = {1122-1134},
	publisher = {Department of Computer Science},
	address = {University of British Columbia, Vancouver},
	abstract = {We study recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when partial support information is available. We show that if at least 50\% of the (partial) support information is accurate, then weighted $\ell_1$ minimization is stable and robust under weaker sufficient conditions than the analogous conditions for standard $\ell_1$ minimization. Moreover, weighted $\ell_1$ minimization provides better upper bounds on the reconstruction error in terms of the measurement noise and the compressibility of the signal to be recovered. We illustrate our results with extensive numerical experiments on synthetic data and real audio and video signals.},
	keywords = {Compressive Sensing},
	doi = {10.1109/TIT.2011.2167214},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEETransInformationTheory/2012/mansour2012IEEETITrcs/mansour2012IEEETITrcs.pdf},
	author = {Michael P. Friedlander and Hassan Mansour and Rayan Saab and Ozgur Yilmaz}
}
@conference {mansour2011SBGFcspsma,
	title = {A compressive sensing perspective on simultaneous marine acquisition},
	booktitle = {SBGF},
	year = {2011},
	publisher = {SBGF},
	organization = {SBGF},
	abstract = {The high cost of acquiring seismic data in marine environments compels the adoption of simultaneous- source acquisition - an emerging technology that is stimulating both geophysical research and commercial efforts. In this paper, we discuss the properties of randomized simultaneous acquisition matrices and demonstrate that sparsity-promoting recovery improves the quality of the reconstructed seismic data volumes. Simultaneous marine acquisition calls for the development of a new set of design principles and post-processing tools. Leveraging established findings from the field of compressed sensing, the recovery from simultaneous sources depends on a sparsifying transform that compresses seismic data, is fast, and reasonably incoherent with the compressive sampling matrix. To achieve this incoherence, we use random time dithering where sequential acquisition with a single airgun is replaced by continuous acquisition with multiple airguns firing at random times and at random locations. We demonstrate our results with simulations of simultaneous Marine acquisition using periodic and randomized time dithering.},
	keywords = {Acquisition, Compressive Sensing, Presentation, SBGF},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SBGF/2011/Mansour11SBGFcspsma/Mansour11SBGFcspsma.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SBGF/2011/Mansour11SBGFcspsma/Mansour11SBGFcspsma.pdf},
	author = {Hassan Mansour and Haneet Wason and Tim T.Y. Lin and Felix J. Herrmann}
}
@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 {wason2011SEGsprsd,
	title = {Sparsity-promoting recovery from simultaneous data: a compressive sensing approach},
	booktitle = {SEG Technical Program Expanded Abstracts},
	volume = {30},
	year = {2011},
	month = {09},
	pages = {6-10},
	publisher = {SEG},
	organization = {SEG},
	abstract = {Seismic data acquisition forms one of the main bottlenecks in seismic imaging and inversion. The high cost of acquisition work and collection of massive data volumes compel the adoption of simultaneous-source seismic data acquisition - an emerging technology that is developing rapidly, stimulating both geophysical research and commercial efforts. Aimed at improving the performance of marine- and land-acquisition crews, simultaneous acquisition calls for development of a new set of design principles and post-processing tools. Leveraging developments from the field of compressive sensing the focus here is on simultaneous-acquisition design and sequential-source data recovery. Apart from proper compressive sensing sampling schemes, the recovery from simultaneous simulations depends on a sparsifying transform that compresses seismic data, is fast, and reasonably incoherent with the compressive-sampling matrix. Using the curvelet transform, in which seismic data can be represented parsimoniously, the recovery of the sequential-source data volumes is achieved using the sparsity-promoting program {\textemdash} SPGL1, a solver based on projected spectral gradients. The main outcome of this approach is a new technology where acquisition related costs are no longer determined by the stringent Nyquist sampling criteria.},
	keywords = {Acquisition, Compressive Sensing, Presentation, SEG},
	doi = {10.1190/1.3628174},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/wason11SEGsprsd/wason11SEGsprsd.pdf},
	presentation = {https://slim.gatech.edu/Publications/Public/Conferences/SEG/2011/wason11SEGsprsd/wason11SEGsprsd_pres.pdf},
	author = {Haneet Wason and Felix J. Herrmann and Tim T.Y. Lin}
}
@conference {Mansour11TRwmmw,
	title = {Weighted -$\ell_1$ minimization with multiple weighting sets},
	booktitle = {Proc. SPIE},
	volume = {8138},
	year = {2011},
	month = {09},
	pages = {813809-813809-13},
	abstract = {In this paper, we study the support recovery conditions of weighted -$\ell_1$ minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify a class of signals for which the recovered vector from -$\ell_1$ minimization provides an accurate support estimate. We then derive stability and robustness guarantees for the weighted -$\ell_1$ minimization problem with more than one support estimate. We show that applying a smaller weight to support estimate that enjoy higher accuracy improves the recovery conditions compared with the case of a single support estimate and the case with standard, i.e., non-weighted,-$\ell_1$ minimization. Our theoretical results are supported by numerical simulations on synthetic signals and real audio signals.},
	keywords = {Compressive Sensing, Optimization},
	doi = {10.1117/12.894165},
	url = {https://slim.gatech.edu/Publications/Public/Conferences/SPIE/2011/Mansour11TRwmmw/Mansour11TRwmmw.pdf},
	author = {Hassan Mansour and Ozgur Yilmaz}
}
@article {herrmann2010GEOPrsg,
	title = {Randomized sampling and sparsity: getting more information from fewer samples},
	journal = {Geophysics},
	volume = {75},
	number = {6},
	year = {2010},
	month = {12},
	pages = {WB173-WB187},
	publisher = {SEG},
	abstract = {Many seismic exploration techniques rely on the collection of massive data volumes that are subsequently mined for information during processing. Although this approach has been extremely successful in the past, current efforts toward higher-resolution images in increasingly complicated regions of the earth continue to reveal fundamental shortcomings in our workflows. Chiefly among these is the so-called {\textquotedblleft}curse of dimensionality{\textquotedblright} exemplified by Nyquist{\textquoteright}s sampling criterion, which disproportionately strains current acquisition and processing systems as the size and desired resolution of our survey areas continue to increase. We offer an alternative sampling method leveraging recent insights from compressive sensing toward seismic acquisition and processing for data that are traditionally considered to be undersampled. The main outcome of this approach is a new technology where acquisition and processing related costs are no longer determined by overly stringent sampling criteria, such as Nyquist. At the heart of our approach lies randomized incoherent sampling that breaks subsampling related interferences by turning them into harmless noise, which we subsequently remove by promoting transform-domain sparsity. Now, costs no longer grow significantly with resolution and dimensionality of the survey area, but instead depend only on transform-domain sparsity. Our contribution is twofold. First, we demonstrate by means of carefully designed numerical experiments that compressive sensing can successfully be adapted to seismic exploration. Second, we show that accurate recovery can be accomplished for compressively sampled data volumes sizes that exceed the size of conventional transform-domain data volumes by only a small factor. Because compressive sensing combines transformation and encoding by a single linear encoding step, this technology is directly applicable to acquisition and to dimensionality reduction during processing. In either case, sampling, storage, and processing costs scale with transform-domain sparsity. We illustrate this principle by means of number of case studies.},
	keywords = {Acquisition, Compressive Sensing, data acquisition, geophysical techniques, Nyquist criterion, Optimization, sampling methods, seismology, SLIM},
	doi = {10.1190/1.3506147},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2010/herrmann2010GEOPrsg/herrmann2010GEOPrsg.pdf},
	author = {Felix J. Herrmann}
}
@article {saab2008ACHAsrb,
	title = {Sparse recovery by non-convex optimization - instance optimality},
	journal = {Applied and Computational Harmonic Analysis},
	volume = {29},
	number = {1},
	year = {2010},
	month = {07},
	pages = {30-48},
	abstract = {In this note, we address the theoretical properties of $\Delta_p$, a class of compressed sensing decoders that rely on $l^p$ minimization with $p \in (0,1)$ to recover estimates of sparse and compressible signals from incomplete and inaccurate measurements. In particular, we extend the results of Cand{\textquoteleft}es, Romberg and Tao [3] and Wojtaszczyk [30] regarding the decoder $\Delta_1$, based on $\ell^1$ minimization, to $Δp$ with $p \in (0,1)$. Our results are two-fold. First, we show that under certain sufficient conditions that are weaker than the analogous sufficient conditions for $\Delta_1$ the decoders $\Delta_p$ are robust to noise and stable in the sense that they are $(2,p)$ instance optimal. Second, we extend the results of Wojtaszczyk to show that, like $\Delta_1$, the decoders $\Delta_p$ are (2,2) instance optimal in probability provided the measurement matrix is drawn from an appropriate distribution. While the extension of the results of [3] to the setting where $p \in (0,1)$ is straightforward, the extension of the instance optimality in probability result of [30] is non-trivial. In particular, we need to prove that the $LQ_1$ property, introduced in [30], and shown to hold for Gaussian matrices and matrices whose columns are drawn uniformly from the sphere, generalizes to an $LQ_p$ property for the same classes of matrices. Our proof is based on a result by Gordon and Kalton [18] about the Banach-Mazur distances of p-convex bodies to their convex hulls.},
	keywords = {Compressive Sensing, non-convex},
	doi = {10.1016/j.acha.2009.08.002},
	url = {http://www.sciencedirect.com/science/article/pii/S1063520309000864},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/ACHA/2010/saab2008ACHAsrb/saab2008ACHAsrb.pdf},
	author = {Rayan Saab and Ozgur Yilmaz}
}
@article {herrmann2009GEOPcsf,
	title = {Compressive simultaneous full-waveform simulation},
	journal = {Geophysics},
	volume = {74},
	number = {4},
	year = {2009},
	month = {07-08},
	pages = {A35-A40},
	abstract = {The fact that computational complexity of wavefield simulation is proportional to the size of the discretized model and acquisition geometry, and not to the complexity of the simulated wavefield, is a major impediment within seismic imaging. By turning simulation into a compressive sensing problem{\textendash}-where simulated data is recovered from a relatively small number of independent simultaneous sources{\textendash}-we remove this impediment by showing that compressively sampling a simulation is equivalent to compressively sampling the sources, followed by solving a reduced system. As in compressive sensing, this allows for a reduction in sampling rate and hence in simulation costs. We demonstrate this principle for the time-harmonic Helmholtz solver. The solution is computed by inverting the reduced system, followed by a recovery of the full wavefield with a sparsity promoting program. Depending on the wavefield{\textquoteright}s sparsity, this approach can lead to significant cost reductions, in particular when combined with the implicit preconditioned Helmholtz solver, which is known to converge even for decreasing mesh sizes and increasing angular frequencies. These properties make our scheme a viable alternative to explicit time-domain finite-differences.},
	keywords = {Compressive Sensing, full-waveform, Modelling, SLIM},
	doi = {10.1190/1.3115122},
	url = {http://library.seg.org/doi/abs/10.1190/1.3115122},
	url2 = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2009/herrmann2009GEOPcsf/herrmann2009GEOPcsf.pdf},
	author = {Felix J. Herrmann and Yogi A. Erlangga and Tim T.Y. Lin}
}
@article {hennenfent2008GEOPsdw,
	title = {Simply denoise: wavefield reconstruction via jittered undersampling},
	journal = {Geophysics},
	volume = {73},
	number = {3},
	year = {2008},
	month = {05},
	pages = {V19-V28},
	publisher = {SEG},
	abstract = {In this paper, we present a new discrete undersampling scheme designed to favor wavefield reconstruction by sparsity-promoting inversion with transform elements that are localized in the Fourier domain. Our work is motivated by empirical observations in the seismic community, corroborated by recent results from compressive sampling, which indicate favorable (wavefield) reconstructions from random as opposed to regular undersampling. As predicted by theory, random undersampling renders coherent aliases into harmless incoherent random noise, effectively turning the interpolation problem into a much simpler denoising problem. A practical requirement of wavefield reconstruction with localized sparsifying transforms is the control on the maximum gap size. Unfortunately, random undersampling does not provide such a control and the main purpose of this paper is to introduce a sampling scheme, coined jittered undersampling, that shares the benefits of random sampling, while offering control on the maximum gap size. Our contribution of jittered sub-Nyquist sampling proves to be key in the formulation of a versatile wavefield sparsity-promoting recovery scheme that follows the principles of compressive sampling. After studying the behavior of the jittered undersampling scheme in the Fourier domain, its performance is studied for curvelet recovery by sparsity-promoting inversion (CRSI). Our findings on synthetic and real seismic data indicate an improvement of several decibels over recovery from regularly-undersampled data for the same amount of data collected.},
	keywords = {Acquisition, Compressive Sensing, Geophysics, Optimization, Processing, sampling, SLIM},
	doi = {10.1190/1.2841038},
	url = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOsdw/hennenfent08GEOsdw.pdf},
	html_version = {https://slim.gatech.edu/Publications/Public/Journals/Geophysics/2008/hennenfent08GEOsdw/paper_html/paper.html},
	author = {Gilles Hennenfent and Felix J. Herrmann}
}
