Paper
17 September 2005 Generalized L-spline wavelet bases
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Proceedings Volume 5914, Wavelets XI; 59140F (2005) https://doi.org/10.1117/12.617123
Event: Optics and Photonics 2005, 2005, San Diego, California, United States
Abstract
We build wavelet-like functions based on a parametrized family of pseudo-differential operators Lv that satisfy some admissibility and scalability conditions. The shifts of the generalized B-splines, which are localized versions of the Green function of Lv, 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.
© (2005) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Ildar Khalidov, Thierry Blu, and Michael Unser "Generalized L-spline wavelet bases", Proc. SPIE 5914, Wavelets XI, 59140F (17 September 2005); https://doi.org/10.1117/12.617123
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Cited by 12 scholarly publications.
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KEYWORDS
Wavelets

Space operations

Filtering (signal processing)

Chemical elements

Signal processing

Applied mathematics

Biomedical optics

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