The research of optimality property of a kind of multidimensional wavelet pack bases

Wavelet packs have attracted more and more attention, just because they have nice time-frequency location property, more design freedom. In this article, vector-valued wavelet packs for space L²(R^s,C^v) are formulated, which are generalizations of univariate wavelet packs. A novel method for constructing biorthogonal vector-valued multivariate wavelet packets is presented and their properties are investigated by virtue of time-frequency analysis method and operator theory. Three biorthogonality formulas concerning these wavelet packs are constructed. Finally, new Riesz bases of three dimensional vector-valued function space are obtained by designing a series of subspaces of biorthogonal vector -valued wavelet packs.