A wavelet filter enhancement scheme with a fast integral B-wavelet transform and pyramidal multi-B-wavelet algorithm

A construction paradigm is proposed to refine a class of wavelet bases such that the filter characteristics are enhanced. In particular, it is shown that the entire Mth order B-wavelet family belong to this class. Exploiting some recent work, a fast integral wavelet transform is found for the refined B-wavelet family. Moreover, this refined basis can be placed into the setting of a multiresolution analysis that has a multiplicity greater than one. Accordingly, a fast, discrete, pyramidal algorithm is realised.