A Nonlinear Diffusion Model for Image Restoration

In this paper, we study the ill posed Perona-Malik equation of image processing[14] and the regularized P-M model i.e. C-model proposed by Catte et al.[4]. The authors present the convex compound of these two models in the form of the system of partial differential equations. The weak solution for t...

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Bibliographic Details
Published inActa Mathematicae Applicatae Sinica Vol. 32; no. 3; pp. 631 - 646
Main Authors Zhu, Yong-gui, Yu, Xin-yan, Zhang, Bin, Niu, Xiu-xiu
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2016
Springer Nature B.V
EditionEnglish series
Subjects
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
P-M模型
Partial differential equations
Theoretical
偏微分方程
图像处理
图像恢复
扩散模型
种用
算子分裂
非线性
C-model
35R30
65Q05
65M06
weak solutions
65J22
Perona-Malik model
AOS algorithm
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Summary:In this paper, we study the ill posed Perona-Malik equation of image processing[14] and the regularized P-M model i.e. C-model proposed by Catte et al.[4]. The authors present the convex compound of these two models in the form of the system of partial differential equations. The weak solution for the equations is proved in detail. The additive operator splitting （AOS） algorithm for the proposed model is also given. Finally, we show some numeric experimental results on images.
Bibliography:Perona-Malik model; C-model; weak solutions; AOS algorithm
11-2041/O1
In this paper, we study the ill posed Perona-Malik equation of image processing[14] and the regularized P-M model i.e. C-model proposed by Catte et al.[4]. The authors present the convex compound of these two models in the form of the system of partial differential equations. The weak solution for the equations is proved in detail. The additive operator splitting （AOS） algorithm for the proposed model is also given. Finally, we show some numeric experimental results on images.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-016-0592-7