@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}
}
@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 {lopez2015IEEEogl,
	title = {Off-the-grid low-rank matrix recovery and seismic data reconstruction},
	journal = {IEEE Journal of Selected Topics in Signal Processing},
	volume = {10},
	number = {4},
	year = {2016},
	note = {(IEEE Journal of Selected Topics in Signal Processing)},
	month = {06},
	pages = {658-671},
	abstract = {Matrix sensing problems capitalize on the knowledge that a data matrix of interest exhibits low rank properties. This low dimensional structure often arises because the data matrix is obtained by sampling a smooth function on a regular (or structured) grid. However, in many practical situations the measurements are taken on an irregular grid (that is accurately known). This results in an "unstructured data matrix" that is less fit for the low rank model in comparison to its regular counterpart and therefore subject to degraded reconstruction via rank penalization techniques. In this paper, we propose and analyze a modified low-rank matrix recovery work-flow that admits unstructured observations. By incorporating a regularization operator which accurately maps structured data to unstructured data, into the nuclear-norm minimization problem, we are able to compensate for data irregularity. Furthermore, by construction our formulation yields output that is supported on a structured grid. We establish recovery error bounds for our methodology and offer matrix sensing and matrix completion numerical experiments including applications to seismic trace interpolation to demonstrate the potential of the approach.},
	keywords = {data regularization, matrix completion, matrix sensing, nonuniform discrete Fourier transform, nuclear-norm relaxation, seismic data, seismic trace interpolation},
	doi = {10.1109/JSTSP.2016.2555482},
	url = {https://slim.gatech.edu/Publications/Public/Journals/IEEESignalProcessingMagazine/2016/lopez2015IEEEogl/lopez2015IEEEogl.pdf},
	url2 = {http://ieeexplore.ieee.org/xpl/login.jsp?tp=\&arnumber=7454674},
	author = {Oscar Lopez and Rajiv Kumar and Ozgur Yilmaz 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}
}
