Inpainting via High-dimensional Universal Shearlet Systems

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 univer...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2018-08, Vol.156 (1), p.177-209
Main Authors: Amiri, Z., Kamyabi-Gol, R. A.
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Computational Mathematics and Numerical Analysis
Data recovery
Experiments
Hilbert space
Mathematical models
Mathematics
Mathematics and Statistics
Missing data
Partial Differential Equations
Probability Theory and Stochastic Processes
Sparsity
Wavelet analysis
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Summary: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 ℓ 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.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-018-0159-0