Title

Tight Frame Approximations For Gabor And Wavelet Frames

Keywords

Frame; Frame aproximation; Gabor and wavelet frames; Operator algebra; Unitary systems

Abstract

Given a window function which generates a Gabor (resp. wavelet) frame. We consider the best approximation by those window functions that generate normalized tight (or just tight) frames. Using a parameterizations of window functions by certain class of operators in the von Neumann algebras associated with shift operators in time and frequency over certain lattices, we are able to prove that for any window function of a Gabor frame, there exists a unique window function which generates a tight Gabor frame and is the best approximation (among all the tight Gabor frames) for the given window function. More generally, we show that this is true for any frame induced by a projective unitary representation for a group. However, this result is not valid for wavelet frames. We will provide a restricted approximation result for semi-orthogonal wavelet frames.

Publication Date

12-1-2001

Publication Title

Proceedings of SPIE - The International Society for Optical Engineering

Volume

4478

Number of Pages

135-141

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1117/12.449695

Socpus ID

0035765631 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0035765631

This document is currently not available here.

Share

COinS