Recovery of sparsest signals via l(q)-minimization

    Authors

    Q. Y. Sun

    Comments

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    Abbreviated Journal Title

    Appl. Comput. Harmon. Anal.

    Keywords

    Compressive sampling; l(q)-minimization; Sparse signal; RECONSTRUCTION; MINIMIZATION; Mathematics, Applied; Physics, Mathematical

    Abstract

    In this paper, it is proved that every s-sparse vector x is an element of R-n can be exactly recovered from the measurement vector z = Ax is an element of R-m via some l(q)-minimization with 0 < q < = 1, as soon as each s-sparse vector x is an element of R-n is uniquely determined by the measurement z. Moreover it is shown that the exponent q in the l(q)-minimization can be so chosen to be about 0.6796 x (1- delta(25)(A)), where delta(25)(A) is the restricted isometry constant of order 2s for the measurement matrix A. (C) 2011 Elsevier Inc. All rights reserved.

    Journal Title

    Applied and Computational Harmonic Analysis

    Volume

    32

    Issue/Number

    3

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    329

    Last Page

    341

    WOS Identifier

    WOS:000301564900002

    ISSN

    1063-5203

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