The Characterization of Orthogonal Matrix-valued Multivariable Wavelet Packets Associated with an Integer-valued Dilation Matrix
Deyou Yuan · 2009
The notion of matrix-valued multiresolution analysis of space of matrix-valued higher-dimensional functions is introduced. An approach for constructing orthogonal matrix-valued higher-dimensional wavelet packets is presented 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 L2(Rd,Crtimesr) are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.