The Biorthogonality Property of Vector-Valued Multivariate Wavelet Packets with M-scale
Hongwei Gao, Liping Ding · 2009
In this paper, we introduce a class of vector-valued wavelet packets for vector-valued multivariate function space, which are generalizations of univariate 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(Rs,Cv) from these wavelet packets.