双正交矩阵值小波的设计

Existence and design of biorthogonal matrix-valued wavelets

研究了矩阵值多分辨分析和双正交矩阵值小波。仿照传统的单小波存在性的证明方法,证明了双正交矩阵值尺度函数存在性的充要条件。给出了构造双正交矩阵值小波滤波器的公式,利用这个公式,双正交矩阵值小波可以像双正交单小波一样,小波所对应的高通滤波器可以通过尺度函数所对应的低通滤波器来表达,基于双正交二尺度矩阵滤波器的因式分解公式,提出了构造双正交矩阵值小波的两种设计,并给出实例来说明本文所提出的算法的可行性。

Biorthogonal matrix-valued wavelets have been employed to analyse matrix-valued signals based on matrix multiresolution analysis. The sufficient condition for existence of a biorthogonal matrix-valued scaling function has been established in terms of the corresponding two-scale matrix symbols. Two designs based on factorization of biorthogonal two-scale matrix symbols are presented. In particular, explicit constructing formulations for biorthogonal matrix-valued wavelets are given. With these formulations, highpass filters of biorthogonal matrix-valued wavelets can be given explicitly by lowpass filters. Examples of two-scale matrix filter banks are given.