SOME CLASS OF PARABOLIC SYSTEMS APPLIED TO IMAGE PROCESSING

被引：23

作者：

Afraites, Lekbir ^{[1
]}

Atlas, Abdelghafour ^{[2
]}

Karami, Fahd ^{[3
]}

Meskine, Driss ^{[3
]}

机构：

[1] Univ Sultan Moulay Slimane, Fac Sci & Tech, BP 523, Beni Mellal, Morocco

[2] Univ Cadi Ayyad, Ecole Natl Sci Appl Safi, Route Sidi Bouzid BP 63, Safi, Morocco

[3] Univ Cadi Ayyad, Ecole Super Technol Essaouira, BP 383 Essaouira El Jadida, Essaouira, Morocco

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2016年 / 21卷 / 06期

关键词：

Image denoising; reaction-diffusion system; Orlicz space; Galerkin method; staircase effect; TOTAL VARIATION MINIMIZATION; EDGE-DETECTION; STAIRCASE REDUCTION; EQUATIONS; DECOMPOSITION;

D O I：

10.3934/dcdsb.2016017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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],[21). 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.

引用

页码：1671 / 1687

页数：17

共 32 条

[1] New diffusion models in image processing [J].

Aboulaich, R. ;

Meskine, D. ;

Souissi, A. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (04) :874-882

[2]

Adams R.A., 1975, Sobolev Spaces

[3] IMAGE SELECTIVE SMOOTHING AND EDGE-DETECTION BY NONLINEAR DIFFUSION .2. [J].

ALVAREZ, L ;

LIONS, PL ;

MOREL, JM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1992, 29 (03) :845-866

[4]

Andreu F., 2001, DIFFERENTIAL INTEGRA, V14, P321

[5]

[Anonymous], 2001, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations

[6]

[Anonymous], 1993, DEGENERATE PARABOLIC, DOI DOI 10.1007/978-1-4612-0895-2

[7] The Perona-Malik inequality and application to image denoising [J].

Atlas, A. ;

Karami, F. ;

Meskine, D. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2014, 18 :57-68

[8]

Blomgren P, 1997, INTERNATIONAL CONFERENCE ON IMAGE PROCESSING - PROCEEDINGS, VOL III, P384, DOI 10.1109/ICIP.1997.632128

[9] NON-LINEAR EQUATIONS AND INEQUATIONS IN DUAL VECTORIAL SPACES [J].

BREZIS, H .

ANNALES DE L INSTITUT FOURIER, 1968, 18 (01) :115-&

[10] A class of nonlinear parabolic-hyperbolic equations applied to image restoration [J].

Cao, Yang ;

Yin, Jingxue ;

Liu, Qiang ;

Li, Meihui .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (01) :253-261

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