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Optical Engineering

Gabor-type matric algebra and fast computations of dual and tight Gaborwavelets
Author(s): Sigang Qiu
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Paper Abstract

We investigate a class of Gabor-type matrices and develop simplified Gabor-type matrix operations. The usual matrix-multiplication in the class is proved to be easily performed with O(ab log b)?O(N log N) complexity. Consequently, we are able to propose fast algorithms for determining the inverse of Gabor frame operators and the square roots of the Gabor frame operators as well as the dual Gabor and tight Gabor wavelets. A necessary and sufficient condition is derived for a Gabor triple (g,a,b) to generate a Gabor frame. It is very easy to predetermine the quality of a given (g,a,b) and the stability of Gabor synthesis.

Paper Details

Date Published: 1 January 1997
PDF: 7 pages
Opt. Eng. 36(1) doi: 10.1117/1.601171
Published in: Optical Engineering Volume 36, Issue 1
Show Author Affiliations
Sigang Qiu, Univ. of Connecticut (United States)

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