Tight Frame Approximations For Gabor And Wavelet Frames
Frame; Frame aproximation; Gabor and wavelet frames; Operator algebra; Unitary systems
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.
Proceedings of SPIE - The International Society for Optical Engineering
Number of Pages
Article; Proceedings Paper
Source API URL
Han, Deguang, "Tight Frame Approximations For Gabor And Wavelet Frames" (2001). Scopus Export 2000s. 70.