Image Denoising via Nonlinear Hybrid Diffusion

Image Denoising via Nonlinear Hybrid Diffusion

A nonlinear anisotropic hybrid diffusion equation is discussed for image denoising, which is a combination of mean curvature smoothing and Gaussian heat diffusion. First, we propose a new edge detection indicator, that is, the diffusivity function. Based on this diffusivity function, the new diffusi...

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Main Authors: Xiaoping Ji, Dazhi Zhang, Zhichang Guo, Boying Wu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2013/890157
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spelling doaj-edb6c6c5a2fa46b8b888fad00bbb60282020-11-25T01:09:19ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472013-01-01201310.1155/2013/890157890157Image Denoising via Nonlinear Hybrid DiffusionXiaoping Ji0Dazhi Zhang1Zhichang Guo2Boying Wu3Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaA nonlinear anisotropic hybrid diffusion equation is discussed for image denoising, which is a combination of mean curvature smoothing and Gaussian heat diffusion. First, we propose a new edge detection indicator, that is, the diffusivity function. Based on this diffusivity function, the new diffusion is nonlinear anisotropic and forward-backward. Unlike the Perona-Malik (PM) diffusion, the new forward-backward diffusion is adjustable and under control. Then, the existence, uniqueness, and long-time behavior of the new regularization equation of the model are established. Finally, using the explicit difference scheme (PM scheme) and implicit difference scheme (AOS scheme), we do numerical experiments for different images, respectively. Experimental results illustrate the effectiveness of the new model with respect to other known models.http://dx.doi.org/10.1155/2013/890157
collection DOAJ
language English
format Article
sources DOAJ
author Xiaoping Ji
Dazhi Zhang
Zhichang Guo
Boying Wu
spellingShingle Xiaoping Ji
Dazhi Zhang
Zhichang Guo
Boying Wu
Image Denoising via Nonlinear Hybrid Diffusion
Mathematical Problems in Engineering
author_facet Xiaoping Ji
Dazhi Zhang
Zhichang Guo
Boying Wu
author_sort Xiaoping Ji
title Image Denoising via Nonlinear Hybrid Diffusion
title_short Image Denoising via Nonlinear Hybrid Diffusion
title_full Image Denoising via Nonlinear Hybrid Diffusion
title_fullStr Image Denoising via Nonlinear Hybrid Diffusion
title_full_unstemmed Image Denoising via Nonlinear Hybrid Diffusion
title_sort image denoising via nonlinear hybrid diffusion
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2013-01-01
description A nonlinear anisotropic hybrid diffusion equation is discussed for image denoising, which is a combination of mean curvature smoothing and Gaussian heat diffusion. First, we propose a new edge detection indicator, that is, the diffusivity function. Based on this diffusivity function, the new diffusion is nonlinear anisotropic and forward-backward. Unlike the Perona-Malik (PM) diffusion, the new forward-backward diffusion is adjustable and under control. Then, the existence, uniqueness, and long-time behavior of the new regularization equation of the model are established. Finally, using the explicit difference scheme (PM scheme) and implicit difference scheme (AOS scheme), we do numerical experiments for different images, respectively. Experimental results illustrate the effectiveness of the new model with respect to other known models.
url http://dx.doi.org/10.1155/2013/890157
work_keys_str_mv AT xiaopingji imagedenoisingvianonlinearhybriddiffusion
AT dazhizhang imagedenoisingvianonlinearhybriddiffusion
AT zhichangguo imagedenoisingvianonlinearhybriddiffusion
AT boyingwu imagedenoisingvianonlinearhybriddiffusion
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