Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix

In this paper, the notion of multiple vector-valued multiresolution analysis of space L2(Rs,Cr×r) is introduced. A method for constructing biorthogonal multiple vector-valued wavelet packets in higher dimensions is presented and their properties is 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 space L2(Rs, Cr×r) is obtained by constructing a series of subspaces of biorthogonal multiple vector-valued wavelet packets.