The Properties of Vector-Valued Higher-Dimensional Wavelet Packets

In this paper, we introduce a class of vector-valued wavelet packets of space L2(R^d, R^u), which are generalizations of multivariate 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. Moreover, it is shown how to gain new Riesz bases of space L²(R^d,R^u) from these wavelet packets.