Construction of Filter Banks of Biorthogonal Vector-valued Compactly Supported Wavelets with Three-Scale
Qingjiang Chen, Pingan Wang · 2009
Wavelet analysis has become a popular subject in scientific research for twenty years. It has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this paper, the notion of vector-valued multiresolution analysis is introduced and the definition of the biorthogonal vector-valued wavelets is given. The existence of biorthogonal vector-valued wavelets associated with a pair of biorthogonal vector-valued compactly supported scaling functions is investigated. An algorithm for constructing a class of biorthogonal vector-valued compactly supported wavelet functions is presented by virtue of multiresolution analysis and matrix theory.