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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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2013/890157 |
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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 |
_version_ |
1725179562737795072 |