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Ten Good Reasons for Using Spline Wavelets

M. Unser

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing V, San Diego CA, USA, July 30-August 1, 1997, vol. 3169, pp. 422-431.

The purpose of this note is to highlight some of the unique properties of spline wavelets. These wavelets can be classified in four categories: othogonal (Battle-Lemarié), 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 symmetric 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.

AUTHOR="Unser, M.",
TITLE="Ten Good Reasons for Using Spline Wavelets",
BOOKTITLE="Proceedings of the {SPIE} Conference on Mathematical
        Imaging: {W}avelet Applications in Signal and Image Processing {V}",
address="San Diego CA, USA",
month="July 30-August 1,",

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