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    Computable performance guarantees for compressed sensing matrices

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    Type
    Article
    Authors
    Cho, Myung
    Vijay Mishra, Kumar
    Xu, Weiyu
    KAUST Grant Number
    OCRF-2014-CRG-3
    Date
    2018-02-27
    Online Publication Date
    2018-02-27
    Print Publication Date
    2018-12
    Permanent link to this record
    http://hdl.handle.net/10754/629746
    
    Metadata
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    Abstract
    The null space condition for ℓ1 minimization in compressed sensing is a necessary and sufficient condition on the sensing matrices under which a sparse signal can be uniquely recovered from the observation data via ℓ1 minimization. However, verifying the null space condition is known to be computationally challenging. Most of the existing methods can provide only upper and lower bounds on the proportion parameter that characterizes the null space condition. In this paper, we propose new polynomial-time algorithms to establish upper bounds of the proportion parameter. We leverage on these techniques to find upper bounds and further develop a new procedure—tree search algorithm—that is able to precisely and quickly verify the null space condition. Numerical experiments show that the execution speed and accuracy of the results obtained from our methods far exceed those of the previous methods which rely on linear programming (LP) relaxation and semidefinite programming (SDP).
    Citation
    Cho M, Vijay Mishra K, Xu W (2018) Computable performance guarantees for compressed sensing matrices. EURASIP Journal on Advances in Signal Processing 2018. Available: http://dx.doi.org/10.1186/s13634-018-0535-y.
    Sponsors
    The work of Weiyu Xu is supported by Simons Foundation 318608, KAUST OCRF-2014-CRG-3, NSF DMS-1418737, and NIH 1R01EB020665-01.
    Publisher
    Springer Nature
    Journal
    EURASIP Journal on Advances in Signal Processing
    DOI
    10.1186/s13634-018-0535-y
    ae974a485f413a2113503eed53cd6c53
    10.1186/s13634-018-0535-y
    Scopus Count
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