Existence and Characterization of Affine Binary Pseudoframes with a Binary Filter Functions

The advantages of frames and their promising features in various application have attracted a lot of interest and effort in recent years. In this paper, the notion of affine bivariate pseudo-frames is develop-ed. The notion of a bivariate generalized multiresolution structure (BGMRS) is proposed. A novel method for constructing one BGMRS 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 provide the notion of the pyramid decomposition scheme.