The Properties of a Sort of Multidimensional Wavelet Packets According to an Integer-Valued Dilation Matrix
Wavelet analysis has become a popular subject in scientific research in the past twenty years. In this work, we develop the concept of a class of vector-valued multivarition matrix. A new method for constructing multidimensional vector-valued wavelet packets is formulated. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. There orthogonality formulas regarding the wavelet packets are provided. Orthogonality decomposition relation formulas of the space L2(Rs)r are obtained by constructing a series of subspaces of the vector-valued wavelet packet. Furthermore, several orthonormal wavelet packet bases of space L2(Rs)r are constructed from the wavelet packets.
B. M. Qiao and X. J. Qiao, "The Properties of a Sort of Multidimensional Wavelet Packets According to an Integer-Valued Dilation Matrix", Advanced Materials Research, Vols. 108-111, pp. 1021-1026, 2010