Edge detection with trigonometric polynomial shearlets

Kevin Schober*, Jürgen Prestin, Serhii A. Stasyuk

*Corresponding author for this work


In this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities 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 the 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.

Original languageEnglish
Article number17
JournalAdvances in Computational Mathematics
Issue number1
Publication statusPublished - 02.2021


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