Theses and Dissertations from UMD

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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.Wang, RongrongSubject: search.filters.subject.Information science

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    Global Geometric Conditions on Sensing Matrices for the Success of L1 Minimization Algorithm
    (2013) Wang, Rongrong; Benedetto, John; Czaja, Wojciech; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    Compressed 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.