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Proceedings Paper

Optimal wavelet basis selection for signal representation
Author(s): Yan Zhuang; John S. Baras
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Paper Abstract

We study the problem of choosing the optical wavelet basis with compact support for signal representation and provide a general algorithm for computing the optimal wavelet basis. We first briefly review the multiresolution property of wavelet decomposition and the conditions for generating a basis of compactly supported discrete wavelets in terms of properties of quadrature mirror filter (QMF) banks. We then parametrize the mother wavelet and scaling function through a set of real coefficients. We further introduce the concept of information measure as a distance measure between the signal and its projection onto the subspace spanned by the wavelet basis in which the signal is to be reconstructed. The optimal basis for a given signal is obtained through minimizing this information measure. We have obtained explicitly the sensitivity of dilations and shifts of the mother wavelet with respect to the coefficient set. A systematic approach is developed here to derive the information gradient with respect to the parameter set for a given square integrable signal and the optimal wavelet basis. A gradient-based optimization algorithm is developed in this paper for computing the optimal wavelet basis.

Paper Details

Date Published: 15 March 1994
PDF: 12 pages
Proc. SPIE 2242, Wavelet Applications, (15 March 1994); doi: 10.1117/12.170025
Show Author Affiliations
Yan Zhuang, Univ. of Maryland/College Park (United States)
John S. Baras, Univ. of Maryland/College Park (United States)

Published in SPIE Proceedings Vol. 2242:
Wavelet Applications
Harold H. Szu, Editor(s)

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