The survey of biorthogonal vector-valued multivariate wavelet packets with nine-scale

Abstract

In this paper, we introduce a class of vector-valued wavelet packets of space L²(R^s,C^v), which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued higher-dimensional wavelet packets is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formu-las regarding these wavelet packets are derived. Moreover, it is shown how to obtain new Riesz bases of space L²(R^s,C^v) from these wavelet packets.