Theses and Dissertations from UMD

Permanent URI for this communityhttp://hdl.handle.net/1903/2

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM

More information is available at Theses and Dissertations at University of Maryland Libraries.

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Author: search.filters.author.Zou, Dongmian

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    Nonlinear Analysis of Phase Retrieval and Deep Learning
    (2017) Zou, Dongmian; Balan, Radu V; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Nonlinearity 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.