Generic explicit wavelet tap derivation
Benjamin LaBorde · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1996
This paper describes the continuing work on a new class of wavelets called abc wavelets, first introduced in 1995. The name is drawn from an extra parameter, c, in addition to the conventional ones of a for dilation and b for translation: (Psi) (a,b,c). The method uses discrete wavelets, where explicit solutions exist for 4 and 6 taps. The wavelets are orthogonal and each system of order N has N/2 - 1 vanishing moments, compared with Daubechies which has N/2 vanishing moments. This means that each wavelet class (4 taps, 6 taps, etc.) is not optimally smooth but the advantage is that another degree of freedom exists which can be used as a special lock condition to mimic any particular form, and thus best model the underlying signal. As an additional advantage, each class does include the Daubechies wavelet of the respective order, so nothing is lost; rather the abc wavelets describe supersets of the conventional discrete wavelets. In this paper, the aspect of speed is addressed, exploiting the free form to derive taps supporting a faster transform than the standard fast Mallet transform.