The Properties of Biorthogonal Vector-valued Bivariate Wavelet Packets

In this paper, we introduce a class of vector-valued wavelet packets of space L²(R²)^u, which are generalizations of bivariable wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Furthermore, it is shown how to obtain new Riesz bases of space L²(R²)^u from these wavelet packets.