Some class of parabolic systems applied to image processing

Lekbir  Afraites; Abdelghafour  Atlas; Fahd  Karami; Driss  Meskine

doi:10.3934/dcdsb.2016017

Article Contents

2016, Volume 21, Issue 6: 1671-1687. Doi: 10.3934/dcdsb.2016017

This issue Previous Article Next Article Global-in-time Gevrey regularity solution for a class of bistable gradient flows

Some class of parabolic systems applied to image processing

1.
Faculté des Sciences et Techniques, Université Sultan Moulay Slimane, B.P. 523 Beni-Mellal
2.
Ecole Nationale des Sciences Appliquées de Sa, Université Cadi Ayyad, Route Sidi Bouzid B.P. 63, Safi
3.
Ecole Supérieure de Technologie d'Essaouira, Université Cadi Ayyad, B.P. 383 Essaouira El Jadida, Essaouira

Received: December 31, 2014

Revised: April 30, 2016

Published: July 2016

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Abstract

In this paper, we are interested in the mathematical and numerical study of a variational model derived as Reaction-Diffusion System for image denoising. We use a nonlinear regularization of total variation (TV) operator's, combined with a decomposition approach of $H^{-1}$ norm suggested by Guo and al. ([19],[20]). Based on Galerkin's method, we prove the existence and uniqueness of the solution on Orlicz space for the proposed model. At last, compared experimental results distinctly demonstrate the superiority of our model, in term of removing noise while preserving the edges and reducing staircase effect.

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Mathematics Subject Classification: 35K57, 94A08, 46E30.

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