Authors

Q. Y. Sun

Comments

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Abbreviated Journal Title

SIAM J. Math. Anal.

Keywords

average sampling; ideal sampling; signals with finite rate of; innovation; shift-invariant spaces; SHIFT-INVARIANT SPACES; BAND-LIMITED FUNCTIONS; LANDAU-TYPE THEOREMS; WAVELET SUBSPACES; INFINITE MATRICES; FRAME OPERATOR; LOCALIZATION; OVERCOMPLETENESS; INTERPOLATION; DENSITY; Mathematics, Applied

Abstract

From an average ( ideal) sampling/reconstruction process, the question arises whether the original signal can be recovered from its average (ideal) samples and, if so, how. We consider the above question under the assumption that the original signal comes from a prototypical space modeling signals with a finite rate of innovation, which includes finitely generated shift-invariant spaces, twisted shift-invariant spaces associated with Gabor frames and Wilson bases, and spaces of polynomial splines with nonuniform knots as its special cases. We show that the displayer associated with an average (ideal) sampling/reconstruction process, which has a well-localized average sampler, can be found to be well-localized. We prove that the reconstruction process associated with an average (ideal) sampling process is robust, locally behaved, and finitely implementable, and thus we conclude that the original signal can be approximately recovered from its incomplete average (ideal) samples with noise in real time. Most of our results in this paper are new even for the special case when the original signal comes from a finitely generated shift-invariant space.

Journal Title

Siam Journal on Mathematical Analysis

Volume

38

Issue/Number

5

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

1389

Last Page

1422

WOS Identifier

WOS:000244631400002

ISSN

0036-1410

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