| SIMULTANEOUSLY SPARSE SOLUTIONS TO LINEAR INVERSE PROBLEMS WITH MULTIPLE SYSTEM MATRICES AND A SINGLE OBSERVATION VECTOR. | |
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MedLine Citation:
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PMID: 20445814 Owner: NLM Status: Publisher |
Abstract/OtherAbstract:
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A problem that arises in slice-selective magnetic resonance imaging (MRI) radio-frequency (RF) excitation pulse design is abstracted as a novel linear inverse problem with a simultaneous sparsity constraint. Multiple unknown signal vectors are to be determined, where each passes through a different system matrix and the results are added to yield a single observation vector. Given the matrices and lone observation, the objective is to find a simultaneously sparse set of unknown vectors that approximately solves the system. We refer to this as the multiple-system single-output (MSSO) simultaneous sparse approximation problem. This manuscript contrasts the MSSO problem with other simultaneous sparsity problems and conducts an initial exploration of algorithms with which to solve it. Greedy algorithms and techniques based on convex relaxation are derived and compared empirically. Experiments involve sparsity pattern recovery in noiseless and noisy settings and MRI RF pulse design. |
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Authors:
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Adam C Zelinski; Vivek K Goyal; Elfar Adalsteinsson |
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Publication Detail:
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Type: JOURNAL ARTICLE |
Journal Detail:
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Title: SIAM journal on scientific computing : a publication of the Society for Industrial and Applied Mathematics Volume: 31 ISSN: 1095-7197 ISO Abbreviation: - Publication Date: 2010 Jan |
Date Detail:
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Created Date: 2010-7-13 Completed Date: - Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 9888470 Medline TA: SIAM J Sci Comput Country: - |
Other Details:
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Languages: ENG Pagination: 4533-4579 Citation Subset: - |
Affiliation:
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Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 ( zelinski@mit.edu , vgoyal@mit.edu , elfar@mit.edu ). |
Export Citation:
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Descriptor/Qualifier:
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| Grant Support | |
ID/Acronym/Agency:
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P41 RR014075-01A1//NCRR NIH HHS; R01 EB000790-01A2//NIBIB NIH HHS; R01 EB006847-01A2//NIBIB NIH HHS; R01 EB007942-02//NIBIB NIH HHS |
From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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