Title

Approximations For Gabor And Wavelet Frames

Keywords

Approximation; Frames; Gabor family and Gabor frames; Hilbert spaces; Unitary systems; Wavelet frames

Abstract

Let ψ be a frame vector under the action of a collection of unitary operators script U sign. Motivated by the recent work of Prank, 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.

Publication Date

8-1-2003

Publication Title

Transactions of the American Mathematical Society

Volume

355

Issue

8

Number of Pages

3329-3342

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9947-03-03047-2

Socpus ID

0043246599 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0043246599

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