Existence and characterization of affine bivariate pseudoframes with filter banks

The advantages of frames and their promising features in various application have attracted a lot of interest and effort in recent years. In this work, the notion of affine bivariate pseudoframes is developed. The notion of a bivariate generalized multiresolution structure (BGMRS) is proposed. A new method for constructing one BGMRA of Paley-Wiener subspaces of space L² (R²) is established. The sufficient condition for the existence of affine bivariate pseudoframes with filter banks is provided by means of a generalized multiresolution structure. Finally, we introduce the notion of the pyramid decomposition scheme.