A pseudo-probabilistic approach to the dilation equation for wavelets
Functional Analysis
2017-11-07 v2 Probability
Abstract
The dilation equation arises naturally when using a multiresolution analysis to construct a wavelet basis. We consider solutions in the space of signed measures, which, after normalization, can be viewed as pseudo-probability measures. Using probabilistic ideas as well as a notion of binary expansions, we discuss the existence and absolute continuity of solutions in dimensions one and two, efficiently recovering previous results in two natural cases. A central role is played by the development of two variants of the classical cascade algorithm, which are adapted to the pseudo-probabilistic and elementary number theoretic context.
Cite
@article{arxiv.1710.01364,
title = {A pseudo-probabilistic approach to the dilation equation for wavelets},
author = {Sarah Dumnich and Robert Neel},
journal= {arXiv preprint arXiv:1710.01364},
year = {2017}
}
Comments
19 pages, 3 figures, typos corrected and minor revisions made