Articles

Gabor-type matrix algebra and fast computations of dual and tight Gabor wavelets

[+] Author Affiliations
Sigang Qiu

University of Connecticut Department of Electrical and Systems Engineering 260 Glenbrook Road, U-157 Storrs, Connecticut 06269 sigang@eng2.uconn.edu

Opt. Eng. 36(1), 276-282 (Jan 01, 1997). doi:10.1117/1.601171
History: Received March 22, 1996; Accepted July 31, 1996
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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. © 1997 Society of Photo-Optical Instrumentation Engineers.

Key words: Gabor-type matrix; discrete Gabor transform; Gabor wavelet; dual Gabor wavelet; tight Gabor wavelet.

© 1997 Society of Photo-Optical Instrumentation Engineers

Topics

Matrices ; Wavelets

Citation

Sigang Qiu
"Gabor-type matrix algebra and fast computations of dual and tight Gabor wavelets", Opt. Eng. 36(1), 276-282 (Jan 01, 1997). ; http://dx.doi.org/10.1117/1.601171


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