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Proceedings Paper

Construction of wavelet bases that mimic the behaviour of some given operator
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Paper Abstract

Probably the most important property of wavelets for signal processing is their multiscale derivative-like behavior when applied to functions. In order to extend the class of problems that can profit of wavelet-based techniques, we propose to build new families of wavelets that behave like an arbitrary scale-covariant operator. Our extension is general and includes many known wavelet bases. At the same time, the method takes advantage a fast filterbank decomposition-reconstruction algorithm. We give necessary conditions for the scale-covariant operator to admit our wavelet construction, and we provide examples of new wavelets that can be obtained with our method.

Paper Details

Date Published: 27 September 2007
PDF: 7 pages
Proc. SPIE 6701, Wavelets XII, 67010S (27 September 2007); doi: 10.1117/12.734606
Show Author Affiliations
Ildar Khalidov, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Dimitri Van De Ville, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Thierry Blu, Ecole Polytechnique Fédérale de Lausanne (Switzerland)
Michael Unser, Ecole Polytechnique Fédérale de Lausanne (Switzerland)


Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)

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