The Research into a Two-directional matrix-valued Quarternary Wave Wraps with multi-scale and Applications
Shiheng Wang, Chunyi Jiao · Advances in computer science research · 2015
In this paper, we introduce a class of vector-valued four-dimensional wavelet packets according to a dilation matrix, which are generalizations of univariate wavelet packets.The defini -tion of biorthogonal vector four-dimensional wavelet packets is provided and their biorthogonality quality is researched by means of time-frequency analysis method, vector subdivision scheme and functional analysis method.Three biorthogonality formulas regarding the wavelet packets are es -tablished.Finally, it is shown how to draw new Riesz bases of space 24 () n LR from these wavelet packets.The sufficient condition for the existence of four-dimensional wavelet packets is estab -lished based on the multiresolution analysis method.4 ,