Characteristics of Affine Bivariate Pseudoframes According to a Bivariate Generalized Multiresolution Structure

Frames have become the focus of active research, both in theory and in applications. In the article, the notion of bivariate affine pseudoframes is introduced. The concept of a bivariate generalized multiresolution analysis is proposed. A new approach for designing one GMRA of Paley-Wiener subspaces of L^2({R^2}) is developed. The sufficient condition for the existence of a class of affine pseudoframes with filter banks is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is obtained based on such a generalized multiresolution analysis.