Sampling and reconstruction of signals in a reproducing kernel subspace of L-P(R-d)

    Authors

    M. Z. Nashed;Q. Y. Sun

    Comments

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    Abbreviated Journal Title

    J. Funct. Anal.

    Keywords

    Sampling; Iterative reconstruction algorithm; Reproducing kernel spaces; Idempotent operators; p-Frames; SHIFT-INVARIANT SPACES; INTEGRABLE GROUP-REPRESENTATIONS; FINITE RATE; ATOMIC DECOMPOSITIONS; HILBERT-SPACES; NOISY SAMPLES; ITERATIVE; RECONSTRUCTION; L-P; INNOVATION; SHANNON; Mathematics

    Abstract

    In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of L-p(R-d), 1 < = p < = infinity, associated with an idempotent integral operator whose kernel has certain off-diagonal decay and regularity. The space of p-integrable non-uniform splines and the shift-invariant spaces generated by finitely many localized functions are our model examples of such reproducing kernel subspaces of L-p(R-d). We show that a signal in such reproducing kernel subspaces can be reconstructed in a stable way from its samples taken on a relatively-separated set with sufficiently small gap. We also study the exponential convergence, consistency, and the asymptotic pointwise error estimate of the iterative approximation-projection algorithm and the iterative frame algorithm for reconstructing a signal in those reproducing kernel spaces from its samples with sufficiently small gap. (C) 2009 Elsevier Inc. All rights reserved.

    Journal Title

    Journal of Functional Analysis

    Volume

    258

    Issue/Number

    7

    Publication Date

    1-1-2010

    Document Type

    Article

    Language

    English

    First Page

    2422

    Last Page

    2452

    WOS Identifier

    WOS:000274216300007

    ISSN

    0022-1236

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