Tight frame approximations for Gabor and wavelet frames

Deguang Han

doi:10.1117/12.449695

5 December 2001 Tight frame approximations for Gabor and wavelet frames

Deguang Han

Proceedings Volume 4478, Wavelets: Applications in Signal and Image Processing IX; (2001) https://doi.org/10.1117/12.449695
Event: International Symposium on Optical Science and Technology, 2001, San Diego, CA, United States

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.

Citation Download Citation

Deguang Han "Tight frame approximations for Gabor and wavelet frames", Proc. SPIE 4478, Wavelets: Applications in Signal and Image Processing IX, (5 December 2001); https://doi.org/10.1117/12.449695

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