Discussion of Properties of a Class of Three-dimensional Wavelet Packets with Five-scale Dilation

In this paper, we introduce a class of biorthogonal vector wavelet packets for vector-valued multivariate function space, which are generalizations of univariate wavelet packets. A procedure for constructing a class of biorthogonal vector wavelet packets in higher dimensions is presented and their biorthogonality property is characterized by virtue of matrix theory, time-frequency analysis method. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space $L^2(R^3,C^{u})$ from these wavelet packets.