The description of dual bivariate pseudoframes with integer-valued grid translation and filter banks

The rise of frame theory in applied mathematics is due to the flexibility and redundancy of frames. In the work, the notion of bivariate affine pseudoframes is introduced and a class of a bivariate generalized multiresolution analysis (GMRA) is introduced. A new approach for constructing one GMRA of Paley-Wiener subspaces of L² (R²) is provided. The sufficient condition for the existence of a sort of affine 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. The existence of biorthogonal vector wavelets is discussed by means of paraunitary vector filter bank theory.