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    block this user Michael Elad Trusted member

    Professor

    Technion - Israel institute of Technology

    A Generalized Uncertainty Principle and Sparse Representation in Pairs of Bases

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    An elementary proof of a basic uncertainty principle concerning pairs of representations of # N vectors in di#erent orthonormal bases is provided. The result, slightly stronger than stated before, has a direct impact on the uniqueness property of the sparse representation of such vectors using pairs of orthonormal bases as overcomplete dictionaries. The main contribution in this paper is the improvement of an important result due to Donoho and Huo concerning the replacement of the l 0 optimization problem by a linear programming minimization when searching for the unique sparse representation. 1

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    Title : A Generalized Uncertainty Principle and Sparse Representation in Pairs of Bases
    Abstract : An elementary proof of a basic uncertainty principle concerning pairs of representations of # N vectors in di#erent orthonormal bases is provided. The result, slightly stronger than stated before, has a direct impact on the uniqueness property of the sparse representation of such vectors using pairs of orthonormal bases as overcomplete dictionaries. The main contribution in this paper is the improvement of an important result due to Donoho and Huo concerning the replacement of the l 0 optimization problem by a linear programming minimization when searching for the unique sparse representation. 1
    Subject : unspecified
    Area : Engineering
    Language : English
    Affiliations : 
    Url : http://www-sccm.stanford.edu/%7Eelad/Journals/10_Sparseness_IT.ps
    Doi : 10.1.1.24.1723

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