On construction of multivariate symmetric MRA-based wavelets
Functional Analysis
2012-01-13 v1
Abstract
For an arbitrary matrix dilation, any integer n and any integer/semi-integer c, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for wavelet functions that are point symmetric/antisymmetric and generate frame-like wavelet system providing approximation order n. For any matrix dilations (which are appropriate for axial symmetry group on R^2 in some natural sense) and given integer n, axial symmetric/antisymmetric frame-like wavelet systems providing approximation order n are constructed. Also, for several matrix dilations the explicit construction of highly symmetric frame-like wavelet systems providing approximation order n is presented.
Cite
@article{arxiv.1201.2606,
title = {On construction of multivariate symmetric MRA-based wavelets},
author = {A. Krivoshein},
journal= {arXiv preprint arXiv:1201.2606},
year = {2012}
}