Construction and characterizations of orthogonal vector-valued multivariate wavelet packets

In this paper, the notion of orthogonal vector-valued wavelet packets of the space L2(Rs, Cd) is introduced. A method for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are investigated by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas with respect to the wavelet packets are established. Orthogonal decomposition relation formulas of L2(Rs, Cd) are obtained by constructing a series of subspaces of vector-valued wavelet packets. In particular, it is shown how to construct various orthonormal bases of L2(Rs, Cd) from these wavelet packets.