%% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ %% Created for Rajiv Mittal at 2014-03-23 17:09:09 -0700 %% Saved with string encoding Unicode (UTF-8) @unpublished{aravkin2013SISCLR, Abstract = {Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of rows and columns,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 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 the collaborative filtering problem using the MovieLens 1M, 10M, and Netflix 100M datasets. Then, we use the new method, along with its robust and subspace re-weighted extensions, to obtain high-quality reconstructions for large scale seismic interpolation problems with real data, even in the presence of data contamination.}, Author = {Aleksandr Y. Aravkin and Rajiv Kumar and Hassan Mansour and Ben Recht and Felix J. Herrmann}, Date-Added = {2014-03-24 00:07:04 +0000}, Date-Modified = {2014-03-24 00:08:58 +0000}, Keywords = {denoising, interpolation, robust, SVD-free}, Month = {05}, Title = {Fast methods for denoising matrix completion formulations, with application to robust seismic data interpolation}, Url = {http://arxiv.org/pdf/1302.4886v3.pdf}, Year = {2013}, Bdsk-Url-1 = {http://arxiv.org/abs/1302.4886}} @conference {wason2013EAGEobs, title = {Ocean bottom seismic acquisition via jittered sampling}, booktitle = {EAGE}, year = {2013}, month = {06}, keywords = {Acquisition, blended, deblending, EAGE, interpolation, marine}, doi = {10.3997/2214-4609.20130379}, url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2013/wason2013EAGEobs/wason2013EAGEobs.pdf}, presentation = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/EAGE/2013/wason2013EAGEobs/wason2013EAGEobs_pres.pdf}, author = {Haneet Wason and Felix J. Herrmann} } @article {Mansour11TRssma, title = {Randomized marine acquisition with compressive sampling matrices}, journal = {Geophysical Prospecting}, volume = {60}, number = {4}, year = {2012}, month = {07}, pages = {648-662}, address = {University of British Columbia, Vancouver}, keywords = {curvelet transform, Fourier, Marine acquisition}, doi = {10.1111/j.1365-2478.2012.01075.x}, url = {http://onlinelibrary.wiley.com/doi/10.1111/j.1365-2478.2012.01075.x/abstract}, author = {Hassan Mansour and Haneet Wason and Tim T.Y. Lin and Felix J. Herrmann} } @article{beasley98ana, author = {Craig J. Beasley and Ronald E. Chambers and Zerong Jiang}, collaboration = {}, title = {A new look at simultaneous sources}, publisher = {SEG}, year = {1998}, journal = {SEG Technical Program Expanded Abstracts}, volume = {17}, number = {1}, pages = {133-135}, url = {http://link.aip.org/link/?SGA/17/133/1}, doi = {10.1190/1.1820149} } @inproceedings{deKok2002eage, author= {R.J. de Kok and D. Gillespie}, title= {A Universal Simultaneous Shooting Technique}, organization ={EAGE}, publisher = {Eur. Ass. of Geosc. and Eng., Expanded abstracts}, meeting = {64th Ann. Internat. Mtg.}, year= {2002} } @article{Beasley2008anl, author = {Beasley, Craig J.}, title = {A new look at marine simultaneous sources}, journal = {The Leading Edge}, volume = {27}, number = {7}, pages = {914-917}, doi = {10.1190/1.2954033}, year = {2008}, URL = {http://tle.geoscienceworld.org/cgi/content/abstract/27/7/914}, eprint = {http://tle.geoscienceworld.org/cgi/reprint/27/7/914.pdf} } @article {hennenfent2010GEOPnct, title = {Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach}, journal = {Geophysics}, volume = {75}, number = {6}, year = {2010}, month = {12}, pages = {WB203-WB210}, publisher = {SEG}, url = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/Geophysics/2010/hennenfent2010GEOPnct/hennenfent2010GEOPnct.pdf}, author = {Gilles Hennenfent and Lloyd Fenelon and Felix J. Herrmann} } @article{hampson2008aus, author = {Hampson, Gary and Stefani, Joe and Herkenhoff, Fred}, title = {Acquisition using simultaneous sources}, journal = {The Leading Edge}, volume = {27}, number = {7}, pages = {918-923}, doi = {10.1190/1.2954034}, year = {2008}, abstract = {We present a technique in which two or more shots are acquired during the time it normally takes to acquire one shot. The two (or more) shots are fired in a near simultaneous manner with small random time delays between the component sources. A variety of processing techniques are applied to produce the same seismic images which would have resulted from firing the simultaneous shots separately. These processing techniques rely on coherency of the wavefield in the common-shot domain and unpredictability in the common-receiver, common-offset, and common-midpoint domains. We present results of its application on synthetic 2D, real 2D, and real 3D data from the Gulf of Mexico. These results demonstrate that, in deep water with modest water-bottom reflectivity, no special processing is required, whereas in shallower water with stronger water-bottom reflectivity, the use of shot-separation techniques is necessary. We conclude that this technique can be used robustly to improve source sampling and, for example, to acquire data from a range of azimuths simultaneously. This has important implications for the economics of wide-azimuth acquisition. }, URL = {http://tle.geoscienceworld.org/cgi/content/abstract/27/7/918}, eprint = {http://tle.geoscienceworld.org/cgi/reprint/27/7/918.pdf} } @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}, keywords = {Acquisition, deblending, HSS, marine, Rank, SEG, source separation}, doi = {http://dx.doi.org/10.1190/segam2014-1583.1}, url = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/SEG/2014/wason2014SEGsss/wason2014SEGsss.html}, presentation = {https://www.slim.eos.ubc.ca/Publications/Public/Conferences/SEG/2014/wason2014SEGsss/wason2014SEGsss_pres.pdf}, author = {Haneet Wason and Rajiv Kumar and Aleksandr Y. Aravkin 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}, 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{Berkhout2008cms, author = {Berkhout, A. J.}, title = {Changing the mindset in seismic data acquisition}, journal = {The Leading Edge}, volume = {27}, number = {7}, pages = {924-938}, doi = {10.1190/1.2954035}, year = {2008}, abstract = {Seismic acquisition surveys are designed such that the time intervals between shots are sufficiently large to avoid the tail of the previous source response interfering with the next one (zero overlap in time). To economize on survey time and processing effort, the current compromise is to keep the number of shots to some acceptable minimum. The result is that in current practice the source domain is poorly sampled. }, URL = {http://tle.geoscienceworld.org/cgi/content/abstract/27/7/924}, eprint = {http://tle.geoscienceworld.org/cgi/reprint/27/7/924.pdf} } @inproceedings{maraschini2012EAGEssi, author = {M. Maraschini and R. Dyer and K. Stevens and D. Bird}, title = {Source Separation by Iterative Rank Reduction - Theory and Applications}, booktitle = {74th EAGE Conference and Exhibition}, year = {2012}, } @article{Keys, author={Keys, R.}, journal={Acoustics, Speech and Signal Processing, IEEE Transactions on}, title={Cubic convolution interpolation for digital image processing}, year={1981}, month={Dec}, volume={29}, number={6}, pages={1153-1160}, keywords={Boundary conditions;Convolution;Digital images;Image converters;Image processing;Image sampling;Interpolation;Kernel;Sampling methods;Signal processing algorithms}, doi={10.1109/TASSP.1981.1163711}, ISSN={0096-3518},} @article{abmakabir, author = {Abma, R. and Kabir, N.}, title = {3D interpolation of irregular data with a POCS algorithm}, journal = {GEOPHYSICS}, volume = {71}, number = {6}, pages = {E91-E97}, year = {2006}, doi = {10.1190/1.2356088}, URL = {http://library.seg.org/doi/abs/10.1190/1.2356088}, eprint = {http://library.seg.org/doi/pdf/10.1190/1.2356088} } @inproceedings{cheng2013SEGsss, author = {Jinkun Cheng and Mauricio D. Sacchi}, title = {Separation of simultaneous source data via iterative rank reduction}, booktitle = {SEG Technical Program Expanded Abstracts}, year = {2013}, pages = {88-93}, url = {http://dx.doi.org/10.1190/segam2013-1313.1} } @phdthesis{kunis06nfft, Author = {S. Kunis}, Date-Added = {2014-03-17 00:43:36 +0000}, Date-Modified = {2014-03-17 00:43:36 +0000}, School = {L{\"u}beck University}, Title = {Nonequispaced FFT: generalisation and inversion}, Year = {2006}} @article{Potts2001, Author = {D. Potts and G. Steidl and M. Tasche}, Chapter = {Fast {F}ourier transforms for nonequispaced data: {A} tutorial}, Date-Added = {2014-03-17 00:43:12 +0000}, Date-Modified = {2014-03-17 00:43:12 +0000}, Editor = {J.J. Benedetto and P.J.S.G. Ferreira}, Number = {12}, Pages = {249-274}, Publisher = {Birkh{\"a}user}, Title = {Modern {S}ampling {T}heory: {M}athematics and {A}pplications}, Year = {2001}} @conference{Li, Author = {C. Li and C. C Mosher and S. T Kaplan}, Publisher = {Society of Exploration Geophysicists}, Title = {Interpolated Compressive Sensing for Seismic Data Reconstruction}, Year = {2012}} @article{hennenfent2006CiSEsdn, Abstract = {The authors present an extension of the fast discrete curvelet transform (FDCT) to nonuniformly sampled data. This extension not only restores curvelet compression rates for nonuniformly sampled data but also removes noise and maps the data to a regular grid.}, Author = {Gilles Hennenfent and Felix J. Herrmann}, Date-Added = {2014-03-17 00:25:55 +0000}, Date-Modified = {2014-03-17 00:25:55 +0000}, Journal = {Computing in Science \& Engineering}, Keywords = {CiSE, Processing}, Month = {05}, Pages = {16 - 25}, Title = {Seismic Denoising with Nonuniformly Sampled Curvelets}, Url = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/CiSE/2006/hennenfent06CiSEsdn/hennenfent06CiSEsdn.pdf}, Volume = {8 Issue:3}, Year = {2006}, Bdsk-Url-1 = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/CiSE/2006/hennenfent06CiSEsdn/hennenfent06CiSEsdn.pdf}} @article{hennenfent2010GEOPnct, Abstract = {We extend our earlier work on the nonequispaced fast discrete curvelet transform (NFDCT) and introduce a second generation of the transform. This new generation differs from the previous one by the approach taken to compute accurate curvelet coefficients from irregularly sampled data. The first generation relies on accurate Fourier coefficients obtained by an l2-regularized inversion of the nonequispaced fast Fourier transform (FFT) whereas the second is based on a direct l1-regularized inversion of the operator that links curvelet coefficients to irregular data. Also, by construction the second generation NFDCT is lossless unlike the first generation NFDCT. This property is particularly attractive for processing irregularly sampled seismic data in the curvelet domain and bringing them back to their irregular record-ing locations with high fidelity. Secondly, we combine the second generation NFDCT with the standard fast discrete curvelet transform (FDCT) to form a new curvelet-based method, coined nonequispaced curvelet reconstruction with sparsity-promoting inversion (NCRSI) for the regularization and interpolation of irregularly sampled data. We demonstrate that for a pure regularization problem the reconstruction is very accurate. The signal-to-reconstruction error ratio in our example is above 40 dB. We also conduct combined interpolation and regularization experiments. The reconstructions for synthetic data are accurate, particularly when the recording locations are optimally jittered. The reconstruction in our real data example shows amplitudes along the main wavefronts smoothly varying with limited acquisition imprint.}, Author = {Gilles Hennenfent and Lloyd Fenelon and Felix J. Herrmann}, Date-Added = {2014-03-17 00:23:43 +0000}, Date-Modified = {2014-03-17 00:23:43 +0000}, Journal = {Geophysics}, Keywords = {curvelet transforms, data acquisition, geophysical techniques, Processing, seismology, SLIM}, Month = {12}, Number = {6}, Pages = {WB203-WB210}, Publisher = {SEG}, Title = {Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach}, Url = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/Geophysics/2010/hennenfent2010GEOPnct/hennenfent2010GEOPnct.pdf}, Volume = {75}, Year = {2010}, Bdsk-Url-1 = {https://www.slim.eos.ubc.ca/Publications/Public/Journals/Geophysics/2010/hennenfent2010GEOPnct/hennenfent2010GEOPnct.pdf}} @article{antil, Author = {Xu, S. and Zhang, Y. and Pham, D. and Lambar{\'e}, G.}, Date-Added = {2014-03-09 05:48:52 +0000}, Date-Modified = {2014-03-09 05:49:02 +0000}, Doi = {10.1190/1.1993713}, Eprint = {http://library.seg.org/doi/pdf/10.1190/1.1993713}, Journal = {GEOPHYSICS}, Number = {4}, Pages = {V87-V95}, Title = {Antileakage Fourier transform for seismic data regularization}, Url = {http://library.seg.org/doi/abs/10.1190/1.1993713}, Volume = {70}, Year = {2005}, Bdsk-Url-1 = {http://library.seg.org/doi/abs/10.1190/1.1993713}, Bdsk-Url-2 = {http://dx.doi.org/10.1190/1.1993713}} @article{651165, Author = {Sacchi, M.D. and Ulrych, T.J. and Walker, C.J.}, Date-Added = {2014-03-09 05:42:48 +0000}, Date-Modified = {2014-03-09 05:42:48 +0000}, Doi = {10.1109/78.651165}, Issn = {1053-587X}, Journal = {Signal Processing, IEEE Transactions on}, Keywords = {Bayes methods;array signal processing;discrete Fourier transforms;estimation theory;extrapolation;geophysical signal processing;harmonic analysis;interference suppression;interpolation;iterative methods;nonparametric statistics;recursive estimation;signal resolution;signal sampling;spectral analysis;Bayes theorem;Cholesky decomposition;Levinson recursion;cost function;extrapolation;gapped data;geophysical data;harmonic retrieval;high-resolution discrete Fourier transform;hyperparameters;interpolation;iterations;iterative nonparametric approach;line spectra;linear event detection;long tailed distribution;noise rejection;objective function;periodogram;phase information;prior distribution;receiver array;sampling;spectral amplitudes;spectral estimation;spectral powers;spectral resolution;time series;Apertures;Cost function;Event detection;Extrapolation;Fourier transforms;Information retrieval;Interpolation;Iterative methods;Sampling methods;Yield estimation}, Month = {Jan}, Number = {1}, Pages = {31-38}, Title = {Interpolation and extrapolation using a high-resolution discrete Fourier transform}, Volume = {46}, Year = {1998}, Bdsk-Url-1 = {http://dx.doi.org/10.1109/78.651165}} @article{abma, Author = {Abma, R. and Claerbout, J.}, Date-Added = {2014-03-09 05:33:58 +0000}, Date-Modified = {2014-03-09 05:35:29 +0000}, Journal = {GEOPHYSICS}, Number = {6}, Pages = {1887-1896}, Title = {Lateral prediction for noise attenuation by t-x and f-x techniques}, Volume = {60}, Year = {1995}, Bdsk-File-1 = 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@article{splitz, Author = {Spitz, S.}, Date-Added = {2014-03-09 05:27:02 +0000}, Date-Modified = {2014-03-09 05:29:14 +0000}, Journal = {GEOPHYSICS}, Number = {6}, Pages = {785-794}, Title = {Seismic trace interpolation in the F-X domain}, Volume = {56}, Year = {1991}, Bdsk-File-1 = 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@inproceedings{Rennie2005, Acmid = {1102441}, Address = {New York, NY, USA}, Author = {Rennie, Jasson D. M. and Srebro, Nathan}, Booktitle = {Proceedings of the 22nd international conference on Machine learning}, Isbn = {1-59593-180-5}, Location = {Bonn, Germany}, Numpages = {7}, Pages = {713--719}, Publisher = {ACM}, Series = {ICML '05}, Title = {Fast maximum margin matrix factorization for collaborative prediction}, Year = {2005}} @article{Bube1997, Author = {Kenneth P. Bube and Robert T. Langan}, Journal = {Geophysics}, Number = {4}, Pages = {1183-1195}, Publisher = {SEG}, Title = {Hybrid $\ell_1/\ell_2$ minimization with applications to tomography}, Volume = {62}, Year = {1997}} @inproceedings{Lee2010, Author = {J. Lee and B. Recht and R. Salakhutdinov and N. Srebro and J. Tropp}, Booktitle = {Advances in Neural Information Processing Systems, 2010}, Title = {Practical Large-Scale Optimization for Max-Norm Regularization}, Year = {2010}} @inproceedings{Srebro2005, Author = {J. D. M. Rennie and N. Srebro}, Booktitle = {ICML '05 Proceedings of the 22nd international conference on Machine learning}, Pages = {713 - 719}, Title = {Fast maximum margin matrix factorization for collaborative prediction.}, Year = {2005}} @article{RechtFazelParrilo2010, Author = {B. Recht and M Fazel and P.A. Parrilo}, Journal = {SIAM Review}, Number = {3}, Pages = {471-501}, Title = {Guaranteed Minimum Rank Solutions to Linear Matrix Equations via Nuclear Norm Minimization.}, Volume = {52}, Year = {2010}} @article{AravkinBurkeFriedlander:2012, Author = {A.Y. Aravkin and J.V. Burke and M.P. Friedlander}, Journal = {submitted to SIAM J. Opt., arXiv:1211.3724}, Title = {Variational Properties of Value Functions}, Year = {2012}} @article{BergFriedlander:2008, Author = {E. {van den} Berg and M. P. Friedlander}, Journal = {SIAM Journal on Scientific Computing}, Keywords = {basis pursuit, convex program, duality, root-finding, Newton's method, projected gradient, one-norm regularization, sparse solutions}, Number = {2}, Pages = {890-912}, Publisher = {SIAM}, Title = {Probing the Pareto frontier for basis pursuit solutions}, Volume = {31}, Year = {2008}} @article{BergFriedlander:2011, Author = {E. {van den} Berg and M. P. Friedlander}, Journal = {SIAM J. Optimization}, Number = {4}, Pages = {1201--1229}, Title = {Sparse optimization with least-squares constraints}, Volume = {21}, Year = {2011}} @inproceedings{CevherDHB08, Author = {V. Cevher and M. F. Duarte and C. Hegde and R. G. Baraniuk}, Booktitle = {NIPS}, Crossref = {conf/nips/2008}, Pages = {257-264}, Publisher = {MIT Press}, Title = {Sparse Signal Recovery Using Markov Random Fields.}, Year = {2008}, Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGJCVYJHZlcnNpb25YJG9iamVjdHNZJGFyY2hpdmVyVCR0b3ASAAGGoKgHCBMUFRYaIVUkbnVsbNMJCgsMDxJXTlMua2V5c1pOUy5vYmplY3RzViRjbGFzc6INDoACgAOiEBGABIAFgAdccmVsYXRpdmVQYXRoWWFsaWFzRGF0YV8QMy4uLy4uLy4uLy4uLy4uLy4uLy4uL0Rvd25sb2Fkcy9zZWdfZ3B5c2E3NzBfVjg3LmJpYtIXCxgZV05TLmRhdGFPEQGgAAAAAAGgAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADOmBZQSCsAAAAJFr0Uc2VnX2dweXNhNzcwX1Y4Ny5iaWIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABIP0s9BQH4AAAAAAAAAAAAHAAIAAAkgAAAAAAAAAAAAAAAAAAAACURvd25sb2FkcwAAEAAIAADOmHjAAAAAEQAIAADPQbD+AAAAAQAMAAkWvQAJFroAAmR8AAIAQE1hY2ludG9zaCBIRDpVc2VyczoAcmFqaXZtaXR0YWw6AERvd25sb2FkczoAc2VnX2dweXNhNzcwX1Y4Ny5iaWIADgAqABQAcwBlAGcAXwBnAHAAeQBzAGEANwA3ADAAXwBWADgANwAuAGIAaQBiAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAMFVzZXJzL3Jhaml2bWl0dGFsL0Rvd25sb2Fkcy9zZWdfZ3B5c2E3NzBfVjg3LmJpYgATAAEvAAAVAAIAEv//AACABtIbHB0eWiRjbGFzc25hbWVYJGNsYXNzZXNdTlNNdXRhYmxlRGF0YaMdHyBWTlNEYXRhWE5TT2JqZWN00hscIiNcTlNEaWN0aW9uYXJ5oiIgXxAPTlNLZXllZEFyY2hpdmVy0SYnVHJvb3SAAQAIABEAGgAjAC0AMgA3AEAARgBNAFUAYABnAGoAbABuAHEAcwB1AHcAhACOAMQAyQDRAnUCdwJ8AocCkAKeAqICqQKyArcCxALHAtkC3ALhAAAAAAAAAgEAAAAAAAAAKAAAAAAAAAAAAAAAAAAAAuM=}} @article{Fornasier:06, Author = {M. Fornasier}, Journal = {J. Math. Imaging Vis.}, Number = {3}, Pages = {359--373}, Title = {Nonlinear Projection Recovery in Digital Inpainting for Color Image Restoration}, Volume = {24}, Year = {2006}} @article{wakin2006civ, Author = {Wakin, M. and Laska, J. and Duarte, M. and Baron, D. and Sarvotham, S. and Takhar, D. and Kelly, K. and Baraniuk, R.}, Journal = {Proc. Picture Coding Symposium}, Title = {{Compressive imaging for video representation and coding}}, Year = {2006}, Bdsk-File-1 = {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}} @article{MCA3-2005, Author = {J.-L Starck and M. Elad and D. Donoho}, Journal = {IEEE Transaction on Image Processing}, Number = {10}, Title = {Image Decomposition Via the Combination of Sparse Representation and a Variational Approach}, Volume = {14}, Year = {2005}} @article{Elad:08, Author = {Mairal, J. and Elad, M. and Sapiro, G.}, Journal = {IEEE Transactions on Image Processing}, Month = {Jan.}, Number = {1}, Pages = {53-69}, Title = {Sparse Representation for Color Image Restoration}, Volume = {17}, Year = {2008}} @inproceedings{Mansour:ICASSP10, Author = {H. Mansour and R. Saab and P. Nasiopoulos and R. Ward}, Booktitle = {Proc. of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}, Month = {March}, Pages = {778--781}, Title = {Color Image Desaturation Using Sparse Reconstruction}, Year = {2010}} @article{Donoho2006_CS, Author = {D. Donoho}, Journal = {IEEE Transactions on Information Theory}, Number = {4}, Pages = {1289-1306}, Title = {Compressed sensing.}, Volume = {52}, Year = {2006}} @article{candes2006nos, Author = {Cand{\`e}s, E. J. and Tao, T.}, Journal = {Information Theory, IEEE Transactions on}, Month = {dec.}, Number = {12}, Pages = {5406 -5425}, Title = {Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies}, Volume = {52}, Year = {2006}} @article{CandesStable2006, Author = {E. J. Cand{\`e}s and J. Romberg and T. Tao}, Journal = {CPAM}, Number = {8}, Pages = {1207-1223}, Title = {Stable Signal Recovery from Incomplete and Inaccurate Measurements}, Volume = {59}, Year = {2006}} @article{neelamani2010esf, Author = {Neelamani, R. and Krohn, C. E. and Krebs, J. R. and Romberg, J. K. and Deffenbaugh, Max and Anderson, John E.}, Journal = {Geophysics}, Number = {6}, Pages = {WB15-WB27}, Title = {Efficient seismic forward modeling using simultaneous random sources and sparsity}, Volume = {75}, Year = {2010}} @conference{hennenfent2006SEGaos, Author = {G. Hennenfent and F. J. Herrmann}, Booktitle = {SEG Technical Program Expanded Abstracts}, Pages = {2797-2801}, Publisher = {SEG}, Title = {Application of stable signal recovery to seismic data interpolation}, Volume = {25}, Year = {2006}} @article{Herrmann11TRfcd, Address = {University of British Columbia, Vancouver}, Author = {F. J. Herrmann and M. P. Friedlander and O. Yilmaz}, Doi = {10.1109/MSP.2012.2185859}, Issn = {1053-5888}, Journal = {Signal Processing Magazine, IEEE}, Number = {3}, Pages = {88-100}, Title = {Fighting the Curse of Dimensionality: Compressive Sensing in Exploration Seismology}, Volume = {29}, Year = {2012}, Bdsk-Url-1 = {http://dx.doi.org/10.1109/MSP.2012.2185859}} @misc{RechFazeParr:2007, Author = {B. Recht and M. Fazel and P. A. Parrilo}, Howpublished = {arXiv 0706.4138}, Month = {June}, Title = {Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization}, Year = {2007}} @phdthesis{Fazel:2002, Author = {Fazel, M.}, School = {Stanford University}, Title = {{Matrix rank minimization with applications}}, Year = {2002}} @article{Candes2011-JACM, Author = {E. Cand\`{e}s and X. Li and Y. Ma and J. Wright}, Journal = {Journal of the {ACM}}, Month = {May}, Number = {3}, Title = {Robust Principal Component Analysis?}, Volume = {58}, Year = {2011}} @inproceedings{RechtRe:2011, Author = {B. Recht and C. R\'e}, Booktitle = {Optimization Online}, Project = {Victor}, Title = {Parallel Stochastic Gradient Algorithms for Large-Scale Matrix Completion}, Topic = {Optimization Online}, Year = {2011}} @incollection{MaxNorm:NIPS2010, Author = {J. Lee and B. Recht and R. Salakhutdinov and N. Srebro and J. Tropp}, Booktitle = {Advances in Neural Information Processing Systems 23}, Editor = {J. Lafferty and C. K. I. Williams and J. Shawe-Taylor and R.S. Zemel and A. Culotta}, Pages = {1297--1305}, Title = {Practical Large-Scale Optimization for Max-norm Regularization}, Year = {2010}} @article{GPSR:2007, Author = {Figueiredo, M.A.T. and Nowak, R.D. and Wright, S.J.}, Journal = {IEEE Journal of Selected Topics in Signal Processing}, Month = {dec.}, Number = {4}, Pages = {586 -597}, Title = {Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems}, Volume = {1}, Year = {2007}} @article{Mansour:TIT12, Author = {M. Friedlander and H. Mansour and R. Saab and O. Yilmaz}, Journal = {IEEE Transactions on Information Theory}, Month = {January}, Number = {1}, Title = {Recovering Compressively Sampled Signals Using Partial Support Information}, Volume = {58}, Year = {2011}} @article{oropeza:V25, Author = {V. Oropeza and M. Sacchi}, Journal = {Geophysics}, Keywords = {geophysical techniques; Hankel matrices; random noise; seismology}, Number = {3}, Pages = {V25-V32}, Publisher = {SEG}, Title = {Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis}, Volume = {76}, Year = {2011}} @article{Sacci1998, Author = {Sacchi, M.D. and Ulrych, T.J. and Walker, C.J.}, Journal = {Signal Processing, IEEE Transactions on}, Month = {jan}, Number = {1}, Pages = {31 -38}, Title = {Interpolation and extrapolation using a high-resolution discrete Fourier transform}, Volume = {46}, Year = {1998}, Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGJCVYJHZlcnNpb25YJG9iamVjdHNZJGFyY2hpdmVyVCR0b3ASAAGGoKgHCBMUFRYaIVUkbnVsbNMJCgsMDxJXTlMua2V5c1pOUy5vYmplY3RzViRjbGFzc6INDoACgAOiEBGABIAFgAdccmVsYXRpdmVQYXRoWWFsaWFzRGF0YV8QMy4uLy4uLy4uLy4uLy4uLy4uLy4uL0Rvd25sb2Fkcy9zZWdfZ3B5c2E3NzBfVjg3LmJpYtIXCxgZV05TLmRhdGFPEQGgAAAAAAGgAAIAAAxNYWNpbnRvc2ggSEQAAAAAAAAAAAAAAAAAAADOmBZQSCsAAAAJFr0Uc2VnX2dweXNhNzcwX1Y4Ny5iaWIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABIP0s9BQH4AAAAAAAAAAAAHAAIAAAkgAAAAAAAAAAAAAAAAAAAACURvd25sb2FkcwAAEAAIAADOmHjAAAAAEQAIAADPQbD+AAAAAQAMAAkWvQAJFroAAmR8AAIAQE1hY2ludG9zaCBIRDpVc2VyczoAcmFqaXZtaXR0YWw6AERvd25sb2FkczoAc2VnX2dweXNhNzcwX1Y4Ny5iaWIADgAqABQAcwBlAGcAXwBnAHAAeQBzAGEANwA3ADAAXwBWADgANwAuAGIAaQBiAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAMFVzZXJzL3Jhaml2bWl0dGFsL0Rvd25sb2Fkcy9zZWdfZ3B5c2E3NzBfVjg3LmJpYgATAAEvAAAVAAIAEv//AACABtIbHB0eWiRjbGFzc25hbWVYJGNsYXNzZXNdTlNNdXRhYmxlRGF0YaMdHyBWTlNEYXRhWE5TT2JqZWN00hscIiNcTlNEaWN0aW9uYXJ5oiIgXxAPTlNLZXllZEFyY2hpdmVy0SYnVHJvb3SAAQAIABEAGgAjAC0AMgA3AEAARgBNAFUAYABnAGoAbABuAHEAcwB1AHcAhACOAMQAyQDRAnUCdwJ8AocCkAKeAqICqQKyArcCxALHAtkC3ALhAAAAAAAAAgEAAAAAAAAAKAAAAAAAAAAAAAAAAAAAAuM=}} @article{NFFTF, Author = {Herrmann, F. J. and Hennenfent, G.}, Date-Modified = {2014-03-09 05:39:40 +0000}, Issn = {1365-246X}, Journal = {Geophysical Journal International}, Keywords = {Fourier analysis, Wavelet transform, Inverse theory, Spatial analysis, Controlled source seismology, Theoretical seismology}, Number = {1}, Pages = {233--248}, Publisher = {Blackwell Publishing Ltd}, Title = {Non-parametric seismic data recovery with curvelet frames}, Volume = {173}, Year = {2008}, Bdsk-File-1 = {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}} @article{CandesPlan2010, Author = {Candes, E.J. and Plan, Y.}, Journal = {Proceedings of the IEEE}, Month = {june}, Number = {6}, Pages = {925 -936}, Title = {Matrix Completion With Noise}, Volume = {98}, Year = {2010}} @article{mansour12iwr, Author = {H. Mansour and F. J. Herrmann and O. Yilmaz}, Journal = {submitted to Geophysics}, Title = {Improved wavefield reconstruction from randomized sampling via weighted one-norm minimization}, Year = {2012}} @misc{Netflix:2006, Author = {S. Funk}, Month = {December}, Title = {Netflix update: Try this at home}, Url = {http://sifter.org/~simon/journal/20061211.html}, Year = {2006}, Bdsk-Url-1 = {http://sifter.org/~simon/journal/20061211.html}} @article{Gross:2011, Author = {David Gross}, Issue = {3}, Journal = {IEEE Transactions on Information Theory}, Pages = {1548--1566}, Title = {{Recovering Low-Rank Matrices From Few Coefficients in Any Basis}}, Volume = {57}, Year = {2011}} @article{HalkoMT11, Author = {N. Halko and P.-G. Martinsson and J. A. Tropp}, Journal = {SIAM Review}, Number = {2}, Pages = {217-288}, Title = {Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions}, Volume = {53}, Year = {2011}} @article{Liberty18122007, Author = {Liberty, Edo and Woolfe, Franco and Martinsson, Per-Gunnar and Rokhlin, Vladimir and Tygert, Mark}, Doi = {10.1073/pnas.0709640104}, Number = {51}, Pages = {20167-20172}, Title = {Randomized algorithms for the low-rank approximation of matrices}, Volume = {104}, Year = {2007}, Bdsk-Url-1 = {http://dx.doi.org/10.1073/pnas.0709640104}} @conference{eageh2013tuck, Author = {C. Da Silva, F. Herrmann}, Booktitle = {75th EAGE Conference, Extended Abstracts}, Date-Added = {2013-01-14 19:36:52 +0000}, Date-Modified = {2013-01-14 19:39:58 +0000}, Title = {Hierarchical Tucker Tensor Optimization - Applications to 4D Seismic Data Interpolation}, Volume = {Submitted}, Year = {2013}} @conference{kumar2013EAGEsind, Author = {Kumar, R. and Aravkin, A.Y. and Mansour, H. and Recht, B. and Herrmann, F.}, Publisher = {EAGE}, Title = {Seismic data interpolation and denoising using SVD-free low-rank matrix factorization}, Year = {2013}} @article{Sashaarxiv, Author = {A. Y. Aravkin and R. Kumar and H.Mansour and B. Recht and F. Herrmann}, Journal = {arXiv:1302.4886}, Title = {An SVD-free Pareto curve approach to rank minimization}, Year = {2013}} @article{ChandrasekaranDGLP06, Author = {Shiv Chandrasekaran and Patrick Dewilde and M. Gu and W. Lyons and T. Pals}, Citedby = {0}, Cites = {0}, Doi = {http://dx.doi.org/10.1137/050639028}, Journal = {SIAM J. Matrix Analysis Applications}, Number = {1}, Pages = {67-81}, Researchr = {http://researchr.org/publication/ChandrasekaranDGLP06}, Title = {A Fast Solver for HSS Representations via Sparse Matrices}, Volume = {29}, Year = {2006}, Bdsk-Url-1 = {http://dx.doi.org/10.1137/050639028}} @unpublished{bander2012dre, Author = {Bander Jumah and Felix J. Herrmann}, Keywords = {multiples, Optimization, Processing}, Title = {Dimensionality-reduced estimation of primaries by sparse inversion}, Url = {https://www.slim.eos.ubc.ca/Publications/Private/Submitted/Journal/bander2012dre/bander2012dre.pdf}, Year = {2012}, Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGJCVYJHZlcnNpb25YJG9iamVjdHNZJGFyY2hpdmVyVCR0b3ASAAGGoKgHCBMUFRYaIVUkbnVsbNMJCgsMDxJXTlMua2V5c1pOUy5vYmplY3RzViRjbGFzc6INDoACgAOiEBGABIAFgAdccmVsYXRpdmVQYXRoWWFsaWFzRGF0YV8QMi4uLy4uLy4uLy4uLy4uLy4uLy4uL0Rvd25sb2Fkcy9CaWJsaW8tQmlidGV4LTQuYmli0hcLGBlXTlMuZGF0YU8RAZ4AAAAAAZ4AAgAADE1hY2ludG9zaCBIRAAAAAAAAAAAAAAAAAAAAM6YFlBIKwAAAAkWvRNCaWJsaW8tQmlidGV4LTQuYmliAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEwBrz1TFGAAAAAAAAAAAAAcAAgAACSAAAAAAAAAAAAAAAAAAAAAJRG93bmxvYWRzAAAQAAgAAM6YeMAAAAARAAgAAM9VJ4gAAAABAAwACRa9AAkWugACZHwAAgA/TWFjaW50b3NoIEhEOlVzZXJzOgByYWppdm1pdHRhbDoARG93bmxvYWRzOgBCaWJsaW8tQmlidGV4LTQuYmliAAAOACgAEwBCAGkAYgBsAGkAbwAtAEIAaQBiAHQAZQB4AC0ANAAuAGIAaQBiAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAL1VzZXJzL3Jhaml2bWl0dGFsL0Rvd25sb2Fkcy9CaWJsaW8tQmlidGV4LTQuYmliAAATAAEvAAAVAAIAEv//AACABtIbHB0eWiRjbGFzc25hbWVYJGNsYXNzZXNdTlNNdXRhYmxlRGF0YaMdHyBWTlNEYXRhWE5TT2JqZWN00hscIiNcTlNEaWN0aW9uYXJ5oiIgXxAPTlNLZXllZEFyY2hpdmVy0SYnVHJvb3SAAQAIABEAGgAjAC0AMgA3AEAARgBNAFUAYABnAGoAbABuAHEAcwB1AHcAhACOAMMAyADQAnICdAJ5AoQCjQKbAp8CpgKvArQCwQLEAtYC2QLeAAAAAAAAAgEAAAAAAAAAKAAAAAAAAAAAAAAAAAAAAuA=}, Bdsk-Url-1 = {https://www.slim.eos.ubc.ca/Publications/Private/Submitted/Journal/bander2012dre/bander2012dre.pdf}} @article{Engquist2010, Acmid = {1801515}, Address = {Amsterdam, The Netherlands, The Netherlands}, Author = {Engquist, Bj\"{o}rn and Ying, Lexing}, Doi = {10.1016/j.cam.2009.08.036}, Issn = {0377-0427}, Issue_Date = {July, 2010}, Journal = {J. Comput. Appl. Math.}, Keywords = {Fast multipole methods, Helmholtz equation, Multidirectional computation, Multiscale methods, N-body problems, Operator compression, Oscillatory kernels, Random sampling, Scattering problems, Separated representations}, Month = jul, Number = {6}, Numpages = {9}, Pages = {1851--1859}, Publisher = {Elsevier Science Publishers B. V.}, Title = {Fast directional algorithms for the Helmholtz kernel}, Url = {http://dx.doi.org/10.1016/j.cam.2009.08.036}, Volume = {234}, Year = {2010}, Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cam.2009.08.036}} @article{DBLP, Author = {Nathan Halko and Per-Gunnar Martinsson and Joel A. Tropp}, Bibsource = {DBLP, http://dblp.uni-trier.de}, Ee = {http://dx.doi.org/10.1137/090771806}, Journal = {SIAM Review}, Number = {2}, Pages = {217-288}, Title = {Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions}, Volume = {53}, Year = {2011}} @conference{dasilva, Author = {Curt Da Silva and Felix J. Herrmann}, Publisher = {EAGE}, Title = {Hierarchical Tucker Tensor Optimization - Applications to 4D Seismic Data Interpolation}, Year = {2013}} @techreport{rajiv2012SEG, Address = {University of British Columbia, Vancouver}, Author = {Rajiv Kumar and Aleksandr Y. Aravkin and Felix J. Herrmann}, Number = {TR-2012-04}, Publisher = {Department of Earth and Ocean Sciences}, Title = {Fast Methods for Rank Minimization with Applications to Seismic-Data Interpolation}, Year = {2012}}