The characteristics of matrix-valued multidimensional wavelet packets with respect to an integer-valued dilation matrix
Qi Li, Hua Li · 2009
In this paper, the notion of matrix-valued multiresolution analysis of space L2(Rs,Cr×r) is introduced. A method for constructing biorthogonal matrix-valued multidimensional wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas concerning these wavelet packets are obtained. Finally, new Riesz bases of space L2(Rs,Cr×r) is obtained by constructing a series of subspaces of biorthogonal vector-valued wavelet packets.