Title

Convolution, average sampling, and a calderon resolution of the identity for shift-invariant spaces

Authors

Authors

A. Aldroubi; Q. Y. Sun;W. S. Tang

Comments

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Abbreviated Journal Title

J. Fourier Anal. Appl.

Keywords

irregular sampling; Calderon resolution; frames; wavelets; amalgam; spaces; RECONSTRUCTION; SUBSPACES; THEOREMS; FRAMES; Mathematics, Applied

Abstract

In this article, we study three interconnected inverse problems in shift invariant spaces: 1) the convolution/deconvolution problem; 2) the uniformly sampled convolution and the reconstruction problem; 3) the sampled convolution followed by sampling on irregular grid and the reconstruction problem. In all three cases, we study both the stable reconstruction as well as ill-posed reconstruction problems. We characterize the convolutors for stable deconvolution as well as those giving rise to ill-posed deconvolution. We also characterize the convolutors that allow stable reconstruction as well as those giving rise to ill-posed reconstruction from uniform sampling. The connection between stable deconvolution, and stable reconstruction from samples after convolution is subtle, as will be demonstrated by several examples and theorems that relate the two problems.

Journal Title

Journal of Fourier Analysis and Applications

Volume

11

Issue/Number

2

Publication Date

1-1-2005

Document Type

Article

Language

English

First Page

215

Last Page

244

WOS Identifier

WOS:000228171400005

ISSN

1069-5869

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