A splitting algorithm for a novel regularization of Perona-Malik and application to image restoration
Abstract In this paper, we focus on a numerical method of a problem called the Perona-Malik inequality which we use for image denoising. This model is obtained as the limit of the Perona-Malik model and the p-Laplacian operator with p→∞. In Atlas et al., (Nonlinear Anal. Real World Appl 18:57–68, 20...
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doaj-ee7061f4932d4f53a541520dffdfd64d2020-11-24T22:01:11ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61802017-06-01201711910.1186/s13634-017-0484-xA splitting algorithm for a novel regularization of Perona-Malik and application to image restorationFahd Karami0Lamia Ziad1Khadija Sadik2Université Cadi Ayyad, Ecole Supérieure de Technologie d’EssaouiraUniversité Cadi Ayyad, Ecole Supérieure de Technologie d’EssaouiraUniversité Cadi Ayyad, Ecole Supérieure de Technologie d’EssaouiraAbstract In this paper, we focus on a numerical method of a problem called the Perona-Malik inequality which we use for image denoising. This model is obtained as the limit of the Perona-Malik model and the p-Laplacian operator with p→∞. In Atlas et al., (Nonlinear Anal. Real World Appl 18:57–68, 2014), the authors have proved the existence and uniqueness of the solution of the proposed model. However, in their work, they used the explicit numerical scheme for approximated problem which is strongly dependent to the parameter p. To overcome this, we use in this work an efficient algorithm which is a combination of the classical additive operator splitting and a nonlinear relaxation algorithm. At last, we have presented the experimental results in image filtering show, which demonstrate the efficiency and effectiveness of our algorithm and finally, we have compared it with the previous scheme presented in Atlas et al., (Nonlinear Anal. Real World Appl 18:57–68, 2014).http://link.springer.com/article/10.1186/s13634-017-0484-xImage restorationPerona-Malik inequalityp-LaplacianSplitting algorithm |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Fahd Karami Lamia Ziad Khadija Sadik |
spellingShingle |
Fahd Karami Lamia Ziad Khadija Sadik A splitting algorithm for a novel regularization of Perona-Malik and application to image restoration EURASIP Journal on Advances in Signal Processing Image restoration Perona-Malik inequality p-Laplacian Splitting algorithm |
author_facet |
Fahd Karami Lamia Ziad Khadija Sadik |
author_sort |
Fahd Karami |
title |
A splitting algorithm for a novel regularization of Perona-Malik and application to image restoration |
title_short |
A splitting algorithm for a novel regularization of Perona-Malik and application to image restoration |
title_full |
A splitting algorithm for a novel regularization of Perona-Malik and application to image restoration |
title_fullStr |
A splitting algorithm for a novel regularization of Perona-Malik and application to image restoration |
title_full_unstemmed |
A splitting algorithm for a novel regularization of Perona-Malik and application to image restoration |
title_sort |
splitting algorithm for a novel regularization of perona-malik and application to image restoration |
publisher |
SpringerOpen |
series |
EURASIP Journal on Advances in Signal Processing |
issn |
1687-6180 |
publishDate |
2017-06-01 |
description |
Abstract In this paper, we focus on a numerical method of a problem called the Perona-Malik inequality which we use for image denoising. This model is obtained as the limit of the Perona-Malik model and the p-Laplacian operator with p→∞. In Atlas et al., (Nonlinear Anal. Real World Appl 18:57–68, 2014), the authors have proved the existence and uniqueness of the solution of the proposed model. However, in their work, they used the explicit numerical scheme for approximated problem which is strongly dependent to the parameter p. To overcome this, we use in this work an efficient algorithm which is a combination of the classical additive operator splitting and a nonlinear relaxation algorithm. At last, we have presented the experimental results in image filtering show, which demonstrate the efficiency and effectiveness of our algorithm and finally, we have compared it with the previous scheme presented in Atlas et al., (Nonlinear Anal. Real World Appl 18:57–68, 2014). |
topic |
Image restoration Perona-Malik inequality p-Laplacian Splitting algorithm |
url |
http://link.springer.com/article/10.1186/s13634-017-0484-x |
work_keys_str_mv |
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