Construction of wavelet bases that mimic the behaviour of some given operator
Journal
Proceedings of SPIE - The International Society for Optical Engineering
Journal Volume
6701
ISBN
9780819468499
Date Issued
2007-12-01
Author(s)
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.
Subjects
Continuous-time signal processing | Differential operators | Green's functions | Multiresolution analysis | Multiresolution approximation | Splines | Wavelets
Type
conference paper