一类伸缩因子为4的d维矩阵值小波

The Construction of Compactly Supported d-dimensional Matrix-valued Wavelets

小波变换在图像处理中是一项强有力的工具。根据信号多分量的特性,在构造向量值小波和矩阵值小波的应用过程中具有灵活性。文章在L2(Rd,Cn×n)空间中引入对应于4尺度矩阵值尺度函数的矩阵值多分辨分析和矩阵值正交小波的概念,给出了d维矩阵值正交小波存在的充要条件,提供了一类紧支撑d维矩阵值正交小波的构造算法。

Wavelet transform is a powerful tool in image processing.According to multicomponent signals,the construction of vector-valued wavelets and matrix valued wavelets has flexibility in the application process.In this paper,we introduce the notion of matrix-valued orthogonal wavelets and matrix-valued multiresolution analysis with four-scale matrix-valued scaling functions of the space L2(Rd,Cn×n).A necessary and sufficient condition for the d-dimensional Matrix-valued orthogonal wavelets is given.The construction algorithm of a class of compactly supported multivariate d-dimensional Matrix-valued orthogonal wavelets is also given.