Construction of Wavelet Bases That Mimic the Behaviour of Some Given Operator

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.


Published in:
Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet XII, 1, San Diego CA, USA, 67010S-1–67010S-7
Year:
2007
Publisher:
SPIE
Laboratories:




 Record created 2015-09-18, last modified 2018-10-07

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