Research on Solving Algebraic Equation Set of Orthogonal and Biorthogonal Wavelet under Vanishing Moment Constraint
Abstract:
We describe algebraic equation set of constructing orthogonal and biorthogonal wavelet under vanishing moment constraint, and propose a method to solve them. The algebraic equation set consists of two parts: linear equation system and non-linear equation system. We first investigate how to solve the linear equation system, then, use the computational results to simplify the non-linear equation system. The non-linear equation system is equivalent to a non-linear two degree polynomial equation set with smaller scale. We also discuss algorithm implementations and point out some problems to be solved further.


References:

  1. Yankui Sun, Fan Bao, Chen Ding, Research on Solving Algebraic Equation Set of Orthogonal and Biorthogonal Wavelet under Vanishing Moment Constraint.Proceedings of 2007 International Conference on Wavelet Analysis and Pattern Recognition, 1847-1852,2007.

  2. Yankui Sun, Algebraic Construction Method of Discrete Wavelet Filters. Proceedings of the International Computer Conference 2006 on Wavelet Active Media Technology and Information Processing.200-205

  3. 孙延奎,小波分析及其应用,机械工业出版社,2005年3月
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