Nonlinear Analysis of Phase Retrieval and Deep Learning

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dc.contributor.advisorBalan, Radu Ven_US
dc.contributor.authorZou, Dongmianen_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.accessioned2017-06-22T06:24:31Z
dc.date.available2017-06-22T06:24:31Z
dc.date.issued2017en_US
dc.description.abstractNonlinearity causes information loss. The phase retrieval problem, or the phaseless reconstruction problem, seeks to reconstruct a signal from the magnitudes of linear measurements. With a more complicated design, convolutional neural networks use nonlinearity to extract useful features. We can model both problems in a frame-theoretic setting. With the existence of a noise, it is important to study the stability of the phaseless reconstruction and the feature extraction part of the convolutional neural networks. We prove the Lipschitz properties in both cases. In the phaseless reconstruction problem, we show that phase retrievability implies a bi-Lipschitz reconstruction map, which can be extended to the Euclidean space to accommodate noises while remaining to be stable. In the deep learning problem, we set up a general framework for the convolutional neural networks and provide an approach for computing the Lipschitz constants.en_US
dc.identifierhttps://doi.org/10.13016/M2MS2X
dc.identifier.urihttp://hdl.handle.net/1903/19487
dc.language.isoenen_US
dc.subject.pqcontrolledApplied mathematicsen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledElectrical engineeringen_US
dc.subject.pquncontrolledDeep Learningen_US
dc.subject.pquncontrolledFramesen_US
dc.subject.pquncontrolledLipschitz Analysisen_US
dc.subject.pquncontrolledNeural Networken_US
dc.subject.pquncontrolledPhase Retrievalen_US
dc.titleNonlinear Analysis of Phase Retrieval and Deep Learningen_US
dc.typeDissertationen_US

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