Semi- and Bi- orthogonal MRA-type wavelet designs and their fast algorithms

Patrice Abry; Akram Aldroubi

doi:10.1117/12.217601

1 September 1995 Semi- and biorthogonal MRA-type wavelet designs and their fast algorithms

Patrice Abry, Akram Aldroubi

Proceedings Volume 2569, Wavelet Applications in Signal and Image Processing III; (1995) https://doi.org/10.1117/12.217601
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

Often, the Discrete Wavelet Transform is performed and implemented with the Daubechies wavelets, the Battle-Lemarie wavelets or the splines wavelets whereas in continuous time wavelet decomposition a much larger variety of mother wavelets are used. Maintaining the dyadic time-frequency sampling and the recursive pyramidal computational structure, we present various methods to obtain any chosen analyzing wavelet (psi) _w, with some desired shape and properties and which is associated with a semi-orthogonal multiresolution analysis or to a pair of bi-orthogonal multiresolutions. We explain in details how to design one's own wavelet, starting from any given Multiresolution Analysis or any pair of bi-orthogonal multiresolutions. We also explicitly derive, in a very general oblique (or bi-orthogonal) framework, the formulae of the filter bank structure that implements the designed wavelet. We illustrate these wavelet design, techniques with examples that we have programmed with Matlab routines, available upon request.

Citation Download Citation

Patrice Abry and Akram Aldroubi "Semi- and biorthogonal MRA-type wavelet designs and their fast algorithms", Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); https://doi.org/10.1117/12.217601

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