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30 October 1997 Ten good reasons for using spline wavelets
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Abstract
The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: orthogonal (Battle-Lemarie), semi-orthogonal (e.g., B-spline), shift-orthogonal, and biorthogonal (Cohen-Daubechies-Feauveau). Unlike most other wavelet bases, splines have explicit formulae in both the time and frequency domain, which greatly facilitates their manipulation. They allow for a progressive transition between the two extreme cases of a multiresolution: Haar's piecewise constant representation (spline of degree zero) versus Shannon's bandlimited model (which corresponds to a spline of infinite order). Spline wavelets are extremely regular and usually symmetrical or anti-symmetric. They can be designed to have compact support and to achieve optimal time-frequency localization (B-spline wavelets). The underlying scaling functions are the B-splines, which are the shortest and most regular scaling functions of order L. Finally, splines have the best approximation properties among all known wavelets of a given order L. In other words, they are the best for approximating smooth functions.
© (1997) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Michael A. Unser "Ten good reasons for using spline wavelets", Proc. SPIE 3169, Wavelet Applications in Signal and Image Processing V, (30 October 1997); doi: 10.1117/12.292801; https://doi.org/10.1117/12.292801
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