The Properties of Biorthogonal Vector-valued Bivariate Wavelet Packets
Junqiu Wang, Jianguo Wang · 2009
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)ufrom these wavelet packets.