Construction of biorthogonal wavelets starting from any two multiresolutions

摘要

Starting from any two given multiresolution analyses of L/sub 2/, {V/sub j//sup 1/}/sub j/spl isin/Z/ and {V/sub j//sup 2/}/sub j/spl isin/Z/, we construct biorthogonal wavelet bases that are associated with this chosen pair of multiresolutions. Thus, our construction method takes a point of view opposite to the one of Cohen-Daubechies-Feauveau (1992), which starts from a well-choosen pair of biorthogonal discrete filters. In our construction, the necessary and sufficient condition is the nonperpendicularity of the multiresolutions.