Generalized L-spline wavelet bases
Journal
Proceedings of SPIE - The International Society for Optical Engineering
Journal Volume
5914
Date Issued
2005-12-01
Author(s)
Abstract
We build wavelet-like functions based on a parametrized family of pseudo-differential operators Lν- that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green function of Lν-, generate a family of L-spline spaces. These spaces have the approximation order equal to the order of the underlying operator. A sequence of embedded spaces is obtained by choosing a dyadic scale progression a = 2i. The consecutive inclusion of the spaces yields the refinement equation, where the scaling filter depends on scale. The generalized L-wavelets are then constructed as basis functions for the orthogonal complements of spline spaces. The vanishing moment property of conventional wavelets is generalized to the vanishing null space element property. In spite of the scale dependence of the filters, the wavelet decomposition can be performed using an adapted version of Mallat's filterbank algorithm.
Subjects
Continuous-time signal processing | Differential operators | Green's functions | Multiresolution analysis | Multiresolution approximation | Splines | Wavelets
Type
conference paper