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Optical Engineering

Matrix methods of constructing wavelet filters and discrete hyper-wavelet transforms
Author(s): Guoqiu Wang
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Paper Abstract

The Mallat algorithm for finite length signals is equivalent to a matrix transform on vector space, and the transform matrix is a finite 2-circular matrix. As a new concept, a minimal matrix, which is also a 2-circular matrix, is put forward. Through new developments of definitions and theorems for a minimal matrix, new algorithms for constructing wavelets filters are obtained. Employing these algorithms, we give several examples of orthonormal and biorthogonal wavelet filters. The methods avoid using a Z-transform or Fourier transform, so it is relatively simple to construct FIR wavelet filters. Because many filters constructed go beyond traditional wavelets, the new concept of discrete hyperwavelets transforms is put forward. Finally, an application in image compression is discussed briefly.

Paper Details

Date Published: 1 April 2000
PDF: 8 pages
Opt. Eng. 39(4) doi: 10.1117/1.602465
Published in: Optical Engineering Volume 39, Issue 4
Show Author Affiliations
Guoqiu Wang, National Univ. of Defense Technology (China)

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