17 September 2005 Generalized biorthogonal Daubechies wavelets
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Proceedings Volume 5914, Wavelets XI; 59141X (2005) https://doi.org/10.1117/12.616536
Event: Optics and Photonics 2005, 2005, San Diego, California, United States
We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9/7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. We consider a dual pair of such multiresolutions, where the scaling functions at a given scale are mutually biorthogonal with respect to translation. Also, they must have the shortest-possible support while reproducing a given set of exponential polynomials. This constitutes a generalization of the standard polynomial reproduction property. The corresponding refinement filters are derived from the ones that were studied by Dyn et al. in the framework of non-stationary subdivision schemes. By using different factorizations of these filters, we obtain a general family of compactly supported dual wavelet bases of L2. In particular, if the exponential parameters are all zero, one retrieves the standard CDF B-spline wavelets and the 9/7 wavelets. Our generalized description yields equivalent constructions for E-spline wavelets. A fast filterbank implementation of the corresponding wavelet transform follows naturally; it is similar to Mallat's algorithm, except that the filters are now scale-dependent. This new scheme offers high flexibility and is tunable to the spectral characteristics of a wide class of signals. In particular, it is possible to obtain symmetric basis functions that are well-suited for image processing.
© (2005) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Cedric Vonesch, Cedric Vonesch, Thierry Blu, Thierry Blu, Michael Unser, Michael Unser, "Generalized biorthogonal Daubechies wavelets", Proc. SPIE 5914, Wavelets XI, 59141X (17 September 2005); doi: 10.1117/12.616536; https://doi.org/10.1117/12.616536


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