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Simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and Fourier domain-based image processing

We consider the very challenging task of restoring images (i) that have a large number of missing pixels, (ii) whose existing pixels are corrupted by noise, and (iii) that ideally contain both cartoon and texture elements. The combination of these three properties makes this inverse problem a very d...

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Detalles Bibliográficos
Autores principales: Thai, D. H., Gottschlich, C.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6083703/
https://www.ncbi.nlm.nih.gov/pubmed/30109034
http://dx.doi.org/10.1098/rsos.171176
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author Thai, D. H.
Gottschlich, C.
author_facet Thai, D. H.
Gottschlich, C.
author_sort Thai, D. H.
collection PubMed
description We consider the very challenging task of restoring images (i) that have a large number of missing pixels, (ii) whose existing pixels are corrupted by noise, and (iii) that ideally contain both cartoon and texture elements. The combination of these three properties makes this inverse problem a very difficult one. The solution proposed in this manuscript is based on directional global three-part decomposition (DG3PD) (Thai, Gottschlich. 2016 EURASIP. J. Image Video Process. 2016, 1–20 (doi:10.1186/s13640-015-0097-y)) with a directional total variation norm, directional G-norm and ℓ(∞)-norm in the curvelet domain as key ingredients of the model. Image decomposition by DG3PD enables a decoupled inpainting and denoising of the cartoon and texture components. A comparison with existing approaches for inpainting and denoising shows the advantages of the proposed method. Moreover, we regard the image restoration problem from the viewpoint of a Bayesian framework and we discuss the connections between the proposed solution by function space and related image representation by harmonic analysis and pyramid decomposition.
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spelling pubmed-60837032018-08-14 Simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and Fourier domain-based image processing Thai, D. H. Gottschlich, C. R Soc Open Sci Computer Science We consider the very challenging task of restoring images (i) that have a large number of missing pixels, (ii) whose existing pixels are corrupted by noise, and (iii) that ideally contain both cartoon and texture elements. The combination of these three properties makes this inverse problem a very difficult one. The solution proposed in this manuscript is based on directional global three-part decomposition (DG3PD) (Thai, Gottschlich. 2016 EURASIP. J. Image Video Process. 2016, 1–20 (doi:10.1186/s13640-015-0097-y)) with a directional total variation norm, directional G-norm and ℓ(∞)-norm in the curvelet domain as key ingredients of the model. Image decomposition by DG3PD enables a decoupled inpainting and denoising of the cartoon and texture components. A comparison with existing approaches for inpainting and denoising shows the advantages of the proposed method. Moreover, we regard the image restoration problem from the viewpoint of a Bayesian framework and we discuss the connections between the proposed solution by function space and related image representation by harmonic analysis and pyramid decomposition. The Royal Society Publishing 2018-07-25 /pmc/articles/PMC6083703/ /pubmed/30109034 http://dx.doi.org/10.1098/rsos.171176 Text en © 2018 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Computer Science
Thai, D. H.
Gottschlich, C.
Simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and Fourier domain-based image processing
title Simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and Fourier domain-based image processing
title_full Simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and Fourier domain-based image processing
title_fullStr Simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and Fourier domain-based image processing
title_full_unstemmed Simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and Fourier domain-based image processing
title_short Simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and Fourier domain-based image processing
title_sort simultaneous inpainting and denoising by directional global three-part decomposition: connecting variational and fourier domain-based image processing
topic Computer Science
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6083703/
https://www.ncbi.nlm.nih.gov/pubmed/30109034
http://dx.doi.org/10.1098/rsos.171176
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