Existence and Property of Subspace Pseudoframes Associated with a Generalized Multiresolution Analysis

The frame theory has been one of powerful tools for researching into wavelets. In the article, the notion of affine bivariate pseudoframes is introduced. The concept of a bivariate generalized multiresolution analysis is developed. A novel approach for constructing one GMRA of Paley-Wiener subspaces of L²(R²) is presented. The sufficient condition for the existence of a class of pseudoframes with filter banks is obtained by virtue of a generalized multiresolution analysis. The pyramid decomposition scheme is established based on such a generalized multiresolution analysis.