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

Ildar Khalidov; Dimitri Van De Ville; Thierry Blu; Michael Unser

doi:10.1117/12.734606

27 September 2007 Construction of wavelet bases that mimic the behaviour of some given operator

Ildar Khalidov, Dimitri Van De Ville, Thierry Blu, Michael Unser

Proceedings Volume 6701, Wavelets XII; 67010S (2007) https://doi.org/10.1117/12.734606
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

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.

Citation Download Citation

Ildar Khalidov, Dimitri Van De Ville, Thierry Blu, and Michael Unser "Construction of wavelet bases that mimic the behaviour of some given operator", Proc. SPIE 6701, Wavelets XII, 67010S (27 September 2007); https://doi.org/10.1117/12.734606

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