Edge detection with trigonometric polynomial shearlets
Functional Analysis
2021-02-10 v2
Abstract
In this paper we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vall\'{e}e Poussin type wavelets are able to detect singularities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of corresponding inner products. In the proof we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.
Keywords
Cite
@article{arxiv.1912.08634,
title = {Edge detection with trigonometric polynomial shearlets},
author = {Jürgen Prestin and Kevin Schober and Serhii A. Stasyuk},
journal= {arXiv preprint arXiv:1912.08634},
year = {2021}
}