Title

Tight Frame Approximation For Multi-Frames And Super-Frames

Keywords

Approximation; Frames; Gabor frames; Multi-frames and super-frames approximation; Projective unitary systems; Shift-invariant subspaces

Abstract

We consider a generator Φ=(φ1, ... φN) for either a multi-frame or a super-frame generated under the action of a projective unitary representation for a discrete countable group. Examples of such frames include Gabor multi-frames, Gabor super-frames and frames for shift-invariant subspaces. We show that there exists a unique normalized tight multi-frame (resp. super-frame) generator Ψ=(ψ1, ...,ψN) such that ∑j=1N φj-ψj2≤∑ j=1N φj-ψj2 holds for all the normalized tight multi-frame (resp. super-frame) generators η=(η1,..., ηN). We also investigate the similar problems for dual frames and discuss a few applications to Gabor frames and some other frames. © 2004 Elsevier Inc.All rights reserved.

Publication Date

7-1-2004

Publication Title

Journal of Approximation Theory

Volume

129

Issue

1

Number of Pages

78-93

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jat.2004.04.012

Socpus ID

3042736744 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/3042736744

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