Construction of finitely supported biorthogonal wavelets by virtue of multiresolution analysis approach

Aside from the straightforward tensor product construction of Daubechies' wavelets, only a few, specific, construction of multivariate orthonormal wavelet systems exist presently in the literature. In this paper, the notion of biorthogonal vector wavelets is introduced. The existence of finitely supported biorthogonal vector wavelets associated with a pair of biorthogonal finitely supported vector scaling functions is researched. A novel method for designing a class of biorthogonal finitely supported vector wavelet functions is presented by using multiresolution analysis. The biorthogonal compactly supported vector wavelets generalize orthonormal wavelet systems.