Rank $M$ Wavelets with $N$ Vanishing Moments

Authors:
Peter Niels Heller
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
1995

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Abstract

This work generalizes the rank 2 (scale factor of 2) orthogonal wavelet sequences of Daubechies to the case of a rank $M$ wavelet matrix. Several equivalent definitions of $N$th 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.