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    Sparse recovery on Euclidean Jordan algebras

    203461_203461.pdf (371.7Kb)
    Access Status
    Open access
    Authors
    Kong, L.
    Sun, Jie
    Tao, J.
    Xiu, N.
    Date
    2015
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Kong, L. and Sun, J. and Tao, J. and Xiu, N. 2015. Sparse recovery on Euclidean Jordan algebras. Linear Algebra and its Applications. 465: pp. 65-87.
    Source Title
    Linear Algebra and its Applications
    DOI
    10.1016/j.laa.2014.09.018
    ISSN
    00243795
    School
    Department of Mathematics and Statistics
    Remarks

    NOTICE: This is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, Vol. 465 (2015). http://dx.doi.org/10.1016/j.laa.2014.09.018

    URI
    http://hdl.handle.net/20.500.11937/20281
    Collection
    • Curtin Research Publications
    Abstract

    This paper is concerned with the problem of sparse recovery on Euclidean Jordan algebra (SREJA), which includes the sparse signal recovery problem and the low-rank symmetric matrix recovery problem as special cases. We introduce the notions of restricted isometry property (RIP), null space property (NSP), and s-goodness for linear transformations in s-SREJA, all of which provide sufficient conditions for s-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra. Moreover, we show that both the s-goodness and the NSP are necessary and sufficient conditions for exact s-sparse recovery via the nuclear norm minimization on Euclidean Jordan algebra. Applying these characteristic properties, we establish the exact and stable recovery results for solving SREJA problems via nuclear norm minimization.

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