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A Sparsity Enforcing Framework with TVL1 Regularization and its Application in MR Imaging and Source Localization

Abstract The theme for this work is the development of fast numerical algorithms for sparse optimization as well as their applications in medical imaging and source localization using sensor array processing. Due to the recently proposed theory of Compressive Sensing (CS), the $\ell_1$ minimization problem attracts more attention for its ability to exploit sparsity. Traditional interior point methods encounter difficulties in computation for solving the CS applications. In the first part of this work, a fast algorithm based on the augmented Lagrangian method for solving the large-scale TV-$\ell_1$ regularized inverse problem is proposed. Specifically, by taking advantage of the separable structure, the original problem can be approximated via the su... (more)
Created Date 2011
Contributor Shen, Wei (Author) / Mittlemann, Hans D (Advisor) / Renaut, Rosemary A (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Gelb, Anne (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Subject Mathematics
Type Doctoral Dissertation
Extent 146 pages
Language English
Reuse Permissions All Rights Reserved
Note Ph.D. Applied Mathematics 2011
Collaborating Institutions Graduate College / ASU Library
Additional Formats MODS / OAI Dublin Core / RIS

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Description Dissertation/Thesis