The research of orthogonality property of a sort of higher-dimensional wavelet packet bases

The The rise of frame theory in applied mathematics is due to the flexibility and redundancy of frames. In the work, the notion of vector wavelet packets for space L²(R^s, C^u) 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 orthogonality formulas concerning these wavelet packets are provided. Furthermore, new Riesz bases of space L²(R^s, C^u) from these wavelet packets are obtained. The pyramid decomposition scheme is established based on such a generalized multiresolution analysis..