SPLINE WAVELETS WITH BOUNDARY VALUES AND VANISHING MOMENTS

Author:

CHUANG ZHITAO1,LIU YOUMING2

Affiliation:

1. College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, P. R. China

2. Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, P. R. China

Abstract

This paper deals with the construction of spline wavelets on the interval [0, 1], which have zero boundary values and vanishing moments. One begins with some primal scaling functions and their biorthogonal duals. Then desired biorthogonal wavelets are given by the method of Dahmen, Kunoth and Urban. Since the structure of those wavelets looks complicated, one tries to construct those types of wavelets only in primal side finally, without using any dual informations. Some numerical experiments show good effects, although the uniform stability remains to be proved theoretically.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Information Systems,Signal Processing

Reference15 articles.

1. K. Bittner, Wavelets and Splines: Athens 2005, eds. G. Chen and M.J. Lai (Nashboro Press, 2006) pp. 93–104.

2. Local Decomposition of Refinable Spaces and Wavelets

3. Biorthogonal bases of compactly supported wavelets

4. Wavelets on the Interval and Fast Wavelet Transforms

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1. ORTHOGONAL WAVELET TRANSFORM OF SIGNAL BASED ON COMPLEX B-SPLINE BASES;International Journal of Wavelets, Multiresolution and Information Processing;2012-11

2. Anisotropic curl-free wavelet bases on the unit cube;Acta Mathematica Sinica, English Series;2012-10-13

3. BALANCED MULTIWAVELETS ON THE INTERVAL [0,1] WITH ARBITRARY INTEGER DILATION FACTOR a;International Journal of Wavelets, Multiresolution and Information Processing;2012-01

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