The Features of Multiscale Pseudoframes and Gabor Frames According to Bivariate Filter Functions

Abstract

The advantages of wavelet analysis and their promising featu-res in various application have attracted a lot of interest and effort in re-cent years. Frame analysis has become popular much later in sampling theory, time-frequency analysis and wavelet theory. In this work, the notion of the binary generalized multiresolution structure (BGMS) of subspace is proposed. The characteristics of binary multiscale pseudof-rames for subspaces is investigated. The construction of a BGMS of Paley-Wiener subspace ofis studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A constructive method for affine frames of based on a BGMS is established. A method for designing a class of affine bivariate dual frames in bi-dimensional space is presented. The results we obtain gains much improvement.