Title

Approximations for Gabor and wavelet frames

Authors

Authors

D. G. Han

Comments

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Abbreviated Journal Title

Trans. Am. Math. Soc.

Keywords

Hilbert spaces; frames; unitary systems; approximation; Gabor family and; Gabor frames; wavelet frames; WEYL-HEISENBERG FRAMES; ALGEBRAS; SYSTEMS; Mathematics

Abstract

Let psi be a frame vector under the action of a collection of unitary operators U. Motivated by the recent work of Frank, Paulsen and Tiballi and some application aspects of Gabor and wavelet frames, we consider the existence and uniqueness of the best approximation by normalized tight frame vectors. We prove that for any frame induced by a projective unitary representation for a countable discrete group, the best normalized tight frame (NTF) approximation exists and is unique. Therefore it applies to Gabor frames (including Gabor frames for subspaces) and frames induced by translation groups. Similar results hold for semi-orthogonal wavelet frames.

Journal Title

Transactions of the American Mathematical Society

Volume

355

Issue/Number

8

Publication Date

1-1-2003

Document Type

Article

DOI Link

http://dx.doi.org/10.1090/s0002-9947-03-03047-2

Language

English

First Page

3329

Last Page

3342

WOS Identifier

WOS:000182986900018

ISSN

0002-9947

Recommended Citation

"Approximations for Gabor and wavelet frames" (2003). Faculty Bibliography 2000s. 3796.
https://stars.library.ucf.edu/facultybib2000/3796