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
Copyright Status
Unknown
Socpus ID
74449089783 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/74449089783
STARS Citation
Nashed, M. Zuhair and Sun, Qiyu, "Sampling And Reconstruction Of Signals In A Reproducing Kernel Subspace Of LP (RD)" (2010). Scopus Export 2010-2014. 1269.
https://stars.library.ucf.edu/scopus2010/1269