The Characteristics of a Type of Biorthogonal Wavelet Packets with Eight-scale Factor in Higher Dimensions
Song Shu-yun, Ailian Huo · 2010
In this paper, the notion of vector-valued wavelet packets for space L2(Rn)sis introduced, which are generalizations of univariate wavelet packets. A constructive method for a class of biorthogonal vector-valued multivariate wavelet packets is presented and their biorthogonality properties are characterized by virtue of matrix theory, and operator theory. Three biorthogonality formulas concerning these wavelet packets are provided. Furthermore, new Riesz bases of space L2(Rn)sfrom these wavelet packets are obtained.