Rank M Wavelets with N Vanishing Moments
Peter Niels Heller · SIAM Journal on Matrix Analysis and Applications · 1995
This work generalizes the rank 2 (scale factor of 2) orthogonal wavelet sequences of Daubechies to the case of a rank Mwavelet matrix. Several equivalent definitions of Nth order vanishing moments for rank M wavelets are developed. These notions are used to find an explicit formula for rank M wavelet scaling sequences with N vanishing wavelet moments (of degree N in our terminology). A full wavelet matrix (scaling sequence and $M - 1$ wavelet sequences) is constructed, with explicit examples.