The Properties of Multidimensional Semi-Orthogonal Frame Wavelet Packets
Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an integer-valued dilation matrix. A novel method for constructing multi-dimen- -sional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are established. Orthogonality decomposition relation formulas of the space are derived by constructing a series of subspaces of wavelet packets. Finally, one new orthonormal wavelet packet bases of are constructed from these wavelet packets.
Q. J. Chen and Y. Y. Wang, "The Properties of Multidimensional Semi-Orthogonal Frame Wavelet Packets", Key Engineering Materials, Vols. 439-440, pp. 896-901, 2010