Characteristics of a class of vector-valued non-separable higher-dimensional wavelet packet bases

In this paper, we introduce vector-valued non-separable higher-dimensional wavelet packets with an arbitrary integer dilation factor. An approach for constructing vector-valued higher-dimensional wavelet packet bases is proposed. Their characteristics are investigated by means of harmonic analysis method, matrix theory and operator theory, and three orthogonality formulas concerning the wavelet packets are presented. Orthogonal decomposition relation formulas of the space L2ðRnÞp are derived by designing a series of subspaces of the vector-valued wavelet packets. Moreover, several orthonormal wavelet packet bases of L2ðRnÞp are constructed from the wavelet packets. Relation to some physical theories such as E-infinity theory and multifractal theory is also discussed.