CONVOLUTION SAMPLING AND RECONSTRUCTION OF SIGNALS IN A REPRODUCING KERNEL SUBSPACE

    Authors

    M. Z. Nashed; Q. Y. Sun;J. Xian

    Comments

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    Abbreviated Journal Title

    Proc. Amer. Math. Soc.

    Keywords

    Convolution sampling; reproducing kernel subspace; iterative algorithm; error estimate; SHIFT-INVARIANT SPACES; FINITE RATE; ITERATIVE RECONSTRUCTION; NOISY; SAMPLES; BANACH-SPACES; WIENERS LEMMA; INNOVATION; OPERATORS; HILBERT; SHANNON; Mathematics, Applied; Mathematics

    Abstract

    We consider convolution sampling and reconstruction of signals in certain reproducing kernel subspaces of L-p, 1 < = p < = infinity. We show that signals in those subspaces could be stably reconstructed from their convolution samples taken on a relatively separated set with small gap. Exponential convergence and error estimates are established for the iterative approximation-projection reconstruction algorithm.

    Journal Title

    Proceedings of the American Mathematical Society

    Volume

    141

    Issue/Number

    6

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    1995

    Last Page

    2007

    WOS Identifier

    WOS:000326571400015

    ISSN

    0002-9939

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