The characterization of a sort of biorthogonal multivariate matrix wavelet packets according to a dilation matrix

In this paper, the notion of matrix-valued multiresolution analysis is introduced. A method for constructing biorthogonal matrix-valued wavelet packets in higher dimensions is presented and their properties are investigated by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas concerning these wavelet packets are obtained. Finally, new Riesz bases of three dimensional matrix-valued function space are obtained by designing a series of subspaces of biorthogonal matrix wavelet packets.