Recovering Data with Group Sparsity by Alternating Direction Methods

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dc.contributor.advisorZhang, Yinen_US
dc.contributor.advisorYin, Wotaoen_US
dc.contributor.committeeMemberBaraniuk, Richard G.en_US
dc.creatorDeng, Weien_US
dc.date.accessioned2012-09-06T04:29:23Zen_US
dc.date.accessioned2012-09-06T04:29:25Zen_US
dc.date.available2012-09-06T04:29:23Zen_US
dc.date.available2012-09-06T04:29:25Zen_US
dc.date.created2012-05en_US
dc.date.issued2012-09-05en_US
dc.date.submittedMay 2012en_US
dc.date.updated2012-09-06T04:29:25Zen_US
dc.description.abstractGroup sparsity reveals underlying sparsity patterns and contains rich structural information in data. Hence, exploiting group sparsity will facilitate more efficient techniques for recovering large and complicated data in applications such as compressive sensing, statistics, signal and image processing, machine learning and computer vision. This thesis develops efficient algorithms for solving a class of optimization problems with group sparse solutions, where arbitrary group configurations are allowed and the mixed L21-regularization is used to promote group sparsity. Such optimization problems can be quite challenging to solve due to the mixed-norm structure and possible grouping irregularities. We derive algorithms based on a variable splitting strategy and the alternating direction methodology. Extensive numerical results are presented to demonstrate the efficiency, stability and robustness of these algorithms, in comparison with the previously known state-of-the-art algorithms. We also extend the existing global convergence theory to allow more generality.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationDeng, Wei. "Recovering Data with Group Sparsity by Alternating Direction Methods." (2012) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/64676">https://hdl.handle.net/1911/64676</a>.en_US
dc.identifier.slug123456789/ETD-2012-05-141en_US
dc.identifier.urihttps://hdl.handle.net/1911/64676en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectGroup sparsityen_US
dc.subjectAlternating direction methoden_US
dc.subjectAugmented Lagrangianen_US
dc.subjectCompressive sensingen_US
dc.subjectGroup lassoen_US
dc.subjectJoint sparsityen_US
dc.titleRecovering Data with Group Sparsity by Alternating Direction Methodsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentComputational and Applied Mathematicsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Artsen_US
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