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Inpainting via High-dimensional Universal Shearlet Systems

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Abstract

Thresholding and compressed sensing in combination with both wavelet and shearlet transforms have been very successful in inpainting tasks. Recent results have demonstrated that shearlets outperform wavelets in the problem of image inpainting. In this paper, we provide a general framework for universal shearlet systems in high dimensions. This theoretical framework is used to analyze the recovery of missing data via \(\ell^{1} \) minimization in an abstract model situation. In addition, we set up a particular model inspired by seismic data and a box mask to model missing data. Finally, the results of numerical experiments comparing various inpainting methods are presented.

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Acknowledgements

The first author would like to thank Professor Gitta Kutyniok for stimulating discussions and pointing out various references. She is grateful to the department of Mathematics, Technische Universität Berlin for hospitality and Martin Genzel for proofreading the paper.

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Authors and Affiliations

  1. Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran

    Z. Amiri & R. A. Kamyabi-Gol

  2. Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159-91775, Mashhad, Iran

    Z. Amiri & R. A. Kamyabi-Gol

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  1. Z. Amiri
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Correspondence to R. A. Kamyabi-Gol.

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Amiri, Z., Kamyabi-Gol, R.A. Inpainting via High-dimensional Universal Shearlet Systems. Acta Appl Math 156, 177–209 (2018). https://doi.org/10.1007/s10440-018-0159-0

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