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The Characterization of Orthogonal Matrix-valued Multivariable Wavelet Packets Associated with an Integer-valued Dilation Matrix

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 L^2(R^d,C^{r\times r}) are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.