Investigation into Characteristics of Biorthogonal Finitely Supported Nonseparable Ternary Wavelet Wraps

Wavelet analysis, as a very active mathematical branch of the nonlinear science, has drawn many attentions since it appeared. In this paper, the notion of biorthogonal non-separable trivariate wavelet wraps, which is the generalization of biorthogonal univariate wavelet wraps, is introduced. A new procedure for constructing them is presented. Their biorthogonality quality is characterized by the filter function theory and time-frequency analysis. Three orthogonality formulas concerning these wavelet wraps are established. Finally, we provide the pyramid decomposition scheme.