Title

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

Authors

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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