On Characteristics of Biorthogonal Vector-Valued Multivariate Wavelet Packets Associated with a Quantity Dilation Matrix

摘要

Wavelet analysis has been a widely applied one method for analyzing signal. In this work, the notion of vector-valued wavelet packets for space L2(Rn)s is proposed, which are generalizations of univariate wavelet packets. A constructive method for a class of biorthogonal vector-valued multivariate wavelet packets is formulated and their biorthogonality properties are discussed 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)s from these wavelet packets are obtained.