The Characterization of a Sort of Biorthogonal Multivariate Wavelet Packets According to an Integer-valued Dilation Matrix
Jinshuan Ma, Xinxian Tian · 2009
The notion of matrix-valued multiresolution analysis of space of matrix-valued multivariate functions is proposed. An approach for constructing orthogonal matrix-valued multivariate wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal bases of L^2(R^s, C^{r\times r}) are obtained by constructing a series of subspaces of biorthogonal matrix-valued wavelet packets.