LULU operators for functions of continuous argument
Classical Analysis and ODEs
2007-11-14 v1 General Mathematics
Abstract
The LULU operators, well known in the nonlinear multiresolution analysis of sequences, are extended to functions defined on a continuous domain, namely, a real interval. We show that the extended operators replicate the essential properties of their discrete counterparts. More precisely, they form a fully ordered semi-group of four elements, preserve the local trend and the total variation.
Cite
@article{arxiv.0711.1944,
title = {LULU operators for functions of continuous argument},
author = {Roumen Anguelov Carl Rohwer},
journal= {arXiv preprint arXiv:0711.1944},
year = {2007}
}