The Characters of Multiscale Pseudoframes of Subspace According to Binary Filter Functions

The notion of a generalized multiresolution structure and the concept of subspace bivariate affine pseudoframes are introduced. The pyramid decom-position scheme of a generalized multiresolution structure(BGMRS) is established, which is generalization of Mallat’s pyramid algorithm. A necessary and sufficient condition for the existence of the pyramid decomposition scheme of space L 2(R 2) is established. The rise of frame theory in applied mathematics is due to the flexibil-ity and redundancy of frames. The structured frames are much easier to construct than structured orthonormal bases. Moreover, affine binary multiscale pseudoframe expansions of L 2(R 2) are designed by virtue of the pyramid decomposition scheme.