Global Geometric Conditions on Sensing Matrices for the Success of L1 Minimization Algorithm

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dc.contributor.advisorBenedetto, Johnen_US
dc.contributor.advisorCzaja, Wojciechen_US
dc.contributor.authorWang, Rongrongen_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2013-06-28T06:54:35Z
dc.date.available2013-06-28T06:54:35Z
dc.date.issued2013en_US
dc.description.abstractCompressed Sensing concerns a new class of linear data acquisition protocols that are more efficient than the classical Shannon sampling theorem when targeting at signals with sparse structures. In this thesis, we study the stability of a Statistical Restricted Isometry Property and show how this property can be further relaxed while maintaining its sufficiency for the Basis Pursuit algorithm to recover sparse signals. We then look at the dictionary extension of Compressed Sensing where signals are sparse under a redundant dictionary and reconstruction is achieved by the $\ell_1$ synthesis method. By establishing a necessary and sufficient condition for the stability of $\ell_1$ synthesis, we are able to predict this algorithm's performances under different dictionaries. Last, we construct a class of deterministic sensing matrix for the Dirac-Fourier joint dictionary.en_US
dc.identifier.urihttp://hdl.handle.net/1903/14122
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledInformation scienceen_US
dc.subject.pquncontrolledCompresseden_US
dc.subject.pquncontrolleddeterministicen_US
dc.subject.pquncontrolledDictionaryen_US
dc.subject.pquncontrolledFourieren_US
dc.subject.pquncontrolledSensingen_US
dc.titleGlobal Geometric Conditions on Sensing Matrices for the Success of L1 Minimization Algorithmen_US
dc.typeDissertationen_US

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