Study of tight bivariate wavelet frames with multi-scale and application in information science

Abstract

Information science is an interdisciplinary science primarily concer-ned with the analysis, collection, classification, manipulation, storage, retrieval and dissemination of information. Frame theory has been the focus of active research for twenty years, both in theory and applications. In this paper, the notion of the bivariate generalized multiresolution structure of subspace L 2(R 2), which is the generalization of frame multiresolution analysis, is proposed. The biorthogonanality traits on wavelet wraps are researched by using time-frequency analysis approach and variable separation approach. The construction of a bivariate generalized multiresolution structure of Paley-Wiener subspace of L 2(R 2) is studied. The pyramid decomposition scheme is obtained based on such a GMS and a sufficient condition for its existence is provided. A procedure for designing a class of orthogonal vector-valued finitely supported wavelet functions is proposed by virtue of filter bank theory and matrix theory. © 2012 Springer-Verlag GmbH.