Title :
Construction of biorthogonal wavelets starting from any two multiresolutions
Author :
Aldroubi, Akram ; Abry, Patrice ; Unser, Michael
Author_Institution :
Dept. of Math., Vanderbilt Univ., Nashville, TN, USA
fDate :
4/1/1998 12:00:00 AM
Abstract :
Starting from any two given multiresolution analyses of L2 , {Vj1}j∈Z and {Vj2}j∈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
Keywords :
band-pass filters; filtering theory; signal resolution; signal synthesis; wavelet transforms; biorthogonal wavelet bases; biorthogonal wavelets construction; filter banks; multiresolution analysis; multiresolutions nonperpendicularity; necessary condition; sufficient condition; Biomedical imaging; Filtering; Finite impulse response filter; Mathematics; Multiresolution analysis; Shape; Spline; Sufficient conditions; Wavelet analysis; Wavelet transforms;
Journal_Title :
Signal Processing, IEEE Transactions on
