The Biorthogonality Property of the Multidimensional Wavelet Packets with Multi-scale Factor

摘要

In this article, we introduce a sort of vector-valued wavelet packets with multi-scale dilation of space L~2(R~n,C~v), which are generalizations of multivariaale wavelet packets. A method for designing a sort of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality property is characterized by virtue of time-frequency analysis method, matrix theory, and operator theory. Three biorthogonality formulas regarding these wavelet packets are established. Furtherore, it is shown how to obtain new Riesz bases of space L~2(R~nC~v) from these wavelet packets.