矩阵稀疏化中的最优子波滤波器组设计

Optimum wavelet filter bank design for the efficient sparse structure of correlation matrices

以子波滤波器组在矩阵稀疏化中的应用为背景，给出了设计优化（两带）子波滤波器组需要满足的一般性条件和优化子波滤波器组的两种设计方法，它们均是简单的线性规划问题．计算了误差对子波滤波器正交性的影响，给出了一个修正的优化算法，使数值精确度有明显提高．仿真结果表明，优化子波滤波器组在矩阵稀疏化和去相关性方面优于Ｄａｕｂｅｃｈｉｅｓ子波滤波器组．

This paper presents the general conditions for the optimum filter banks which are designed specifically for the computation of sparse matrices. Two designing methods based on simple linear optimization are given and a modified algorithm of high computation precision is presented to reduce the effects of computation error on the orthogonality of wavelet filters. Experimental results show that our filter banks are superior to Daubechies wavelet filter banks in the computation of sparse matrices and decorrelation.