Title

Sampling And Reconstruction Of Signals In A Reproducing Kernel Subspace Of LP (RD)

Keywords

Idempotent operators; Iterative reconstruction algorithm; p-Frames; Reproducing kernel spaces; Sampling

Abstract

In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of Lp (Rd), 1 ≤ p ≤ ∞, 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 Lp (Rd). 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. © 2009 Elsevier Inc. All rights reserved.

Publication Date

4-1-2010

Publication Title

Journal of Functional Analysis

Volume

258

Issue

7

Number of Pages

2422-2452

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jfa.2009.12.012

Socpus ID

74449089783 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/74449089783

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