Abstract
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.
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Acknowledgments
We would like to thank the referees for their valuable comments and remarks.
Funding
The authors were supported by H2020-MSCA-RISE-2014 Project number 645672 (AMMODIT: Approximation Methods for Molecular Modelling and Diagnosis Tools). Open Access funding enabled and organized by Projekt DEAL.
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Communicated by: Gitta Kutyniok
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Schober, K., Prestin, J. & Stasyuk, S.A. Edge detection with trigonometric polynomial shearlets. Adv Comput Math 47, 17 (2021). https://doi.org/10.1007/s10444-020-09838-3
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DOI: https://doi.org/10.1007/s10444-020-09838-3
Keywords
- Detection of step discontinuities
- Trigonometric polynomial shearlets
- Directional wavelets
- Periodic wavelets