@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 = {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} } @article{Recht:2010:GMS:1958515.1958520, author = {Recht, Benjamin and Fazel, Maryam and Parrilo, Pablo A.}, title = {Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization}, journal = {SIAM Rev.}, issue_date = {August 2010}, volume = {52}, number = {3}, month = aug, year = {2010}, issn = {0036-1445}, pages = {471--501}, numpages = {31}, url = {http://dx.doi.org/10.1137/070697835}, doi = {10.1137/070697835}, acmid = {1958520}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia, PA, USA}, keywords = {compressed sensing, convex optimization, matrix norms, random matrices, rank, semidefinite programming}, } @ARTICLE{candes09exact, author = {Cand\`{e}s, Emmanuel and Recht, Benjamin}, title = {Exact Matrix Completion via Convex Optimization}, journal = {Foundations of Computational Mathematics}, year = {2009}, volume = {9}, pages = {717-772}, date-added = {2012-03-06 04:16:00 +0000}, date-modified = {2012-03-06 04:25:53 +0000}, issn = {1615-3375}, issue = {6}, keyword = {Mathematics and Statistics}, publisher = {Springer New York}, url = {http://dx.doi.org/10.1007/s10208-009-9045-5} } @article{DBLP:journals/corr/abs-0903-3131, author = {Emmanuel J. Cand{\`{e}}s and Yaniv Plan}, title = {Matrix Completion With Noise}, journal = {CoRR}, volume = {abs/0903.3131}, year = {2009}, url = {http://arxiv.org/abs/0903.3131}, timestamp = {Mon, 05 Dec 2011 18:04:56 +0100}, biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/abs-0903-3131}, bibsource = {dblp computer science bibliography, http://dblp.org} } @article{doi:10.1137/080714488, author = {van den Berg, E. and Friedlander, M.}, title = {Probing the Pareto Frontier for Basis Pursuit Solutions}, journal = {SIAM Journal on Scientific Computing}, volume = {31}, number = {2}, pages = {890-912}, year = {2009}, doi = {10.1137/080714488}, URL = { http://dx.doi.org/10.1137/080714488 }, eprint = { http://dx.doi.org/10.1137/080714488 } } @TECHREPORT{HerrHenn:2007a, author = {F. J. Herrmann and G. Hennenfent}, title = {Non-parametric seismic data recovery with curvelet frames}, institution = {UBC Earth \& Ocean Sciences Department}, year = 2007, note = {TR-2007-1}, month = {January}, url = {http://slim.eos.ubc.ca/Publications/Public/Journals/CRSI.pdf} } @MISC{Mansour_improvedwavefield, author = {Hassan Mansour and Felix J. Herrmann and Özgür Yılmaz}, title = {Improved wavefield reconstruction from randomized sampling via weighted one-norm}, year = {} } @article{journals/siamjo/CaiCS10, added-at = {2010-07-21T15:54:11.000+0200}, author = {Cai, Jian-Feng and Candès, Emmanuel J. and Shen, Zuowei}, biburl = {http://www.bibsonomy.org/bibtex/281394d59404456fb909adec32753ef92/dblp}, date = {2010-06-24}, ee = {http://dx.doi.org/10.1137/080738970}, interhash = {6cb6845e5623ae65087fea39f385d958}, intrahash = {81394d59404456fb909adec32753ef92}, journal = {SIAM Journal on Optimization}, keywords = {dblp}, number = 4, pages = {1956-1982}, timestamp = {2010-07-21T15:54:11.000+0200}, title = {A Singular Value Thresholding Algorithm for Matrix Completion.}, url = {http://dblp.uni-trier.de/db/journals/siamjo/siamjo20.html#CaiCS10}, volume = 20, year = 2010 } @article{RankMinFazel, author = {Fazel, Maryam}, journal = {Electrical Engineering Department Stanford University}, pages = {1-130}, title = {Matrix rank minimization with applications.}, volume = 54, year = 2002 } @article{Srebrol, author = {Srebro, Nathan}, journal = {Massachusetts Institute of Technology}, title = {Learning with Matrix Factorizations.}, year = 2004 } @inproceedings{Jain:2013:LMC:2488608.2488693, author = {Jain, Prateek and Netrapalli, Praneeth and Sanghavi, Sujay}, title = {Low-rank Matrix Completion Using Alternating Minimization}, booktitle = {Proceedings of the Forty-fifth Annual ACM Symposium on Theory of Computing}, series = {STOC '13}, year = {2013}, isbn = {978-1-4503-2029-0}, location = {Palo Alto, California, USA}, pages = {665--674}, numpages = {10}, url = {http://doi.acm.org/10.1145/2488608.2488693}, doi = {10.1145/2488608.2488693}, acmid = {2488693}, publisher = {ACM}, address = {New York, NY, USA}, keywords = {alternating minimization, matrix completion, matrix sensing}, } @article{DBLP:journals/corr/abs-0909-5457, author = {Raghu Meka and Prateek Jain and Inderjit S. Dhillon}, title = {Guaranteed Rank Minimization via Singular Value Projection}, journal = {CoRR}, volume = {abs/0909.5457}, year = {2009}, url = {http://arxiv.org/abs/0909.5457}, timestamp = {Wed, 05 Jun 2013 19:32:10 +0200}, biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/abs-0909-5457}, bibsource = {dblp computer science bibliography, http://dblp.org} } @conference {kumar2014EAGErank, title = {{SVD}-free low-rank matrix factorization : wavefield reconstruction via jittered subsampling and reciprocity}, booktitle = {EAGE}, 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://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2014/kumar2014EAGErank/kumar2014EAGErank.pdf}, presentation = {https://www.slim.eos.ubc.ca/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} } @article{doi:10.1137/120887795, author = {Xu, Y. and Yin, W.}, title = {A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion}, journal = {SIAM Journal on Imaging Sciences}, volume = {6}, number = {3}, pages = {1758-1789}, year = {2013}, doi = {10.1137/120887795}, URL = { http://dx.doi.org/10.1137/120887795 }, eprint = { http://dx.doi.org/10.1137/120887795 } } @article{osher, author = {Yang Yi and Ma, Jianwei and Osher, Stanley}, journal = {Inverse Problems and Imaging}, pages = {1379 - 1392}, title = {Seismic data reconstruction via matrix completion.}, volume = 7, year = 2013 }