$An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation$
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An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation

The image denoising model based on anisotropic diffusion equation often appears the staircase effect while image denoising, and the traditional super-resolution reconstruction algorithm can not effectively suppress the noise in the image in the case of blur and serious noise. To tackle this problem,...

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Autores principales:	Jimin Yu, Jiajun Yin, Shangbo Zhou, Saiao Huang, Xianzhong Xie
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	anisotropic diffusion equation adaptive gradient fidelity term washout filter image super-resolution reconstruction Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/ad1ca843a6a24216861ae91118500353
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id	oai:doaj.org-article:ad1ca843a6a24216861ae91118500353
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spelling	oai:doaj.org-article:ad1ca843a6a24216861ae911185003532021-11-11T01:58:02ZAn image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation10.3934/mbe.20213261551-0018https://doaj.org/article/ad1ca843a6a24216861ae911185003532021-08-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021326?viewType=HTMLhttps://doaj.org/toc/1551-0018The image denoising model based on anisotropic diffusion equation often appears the staircase effect while image denoising, and the traditional super-resolution reconstruction algorithm can not effectively suppress the noise in the image in the case of blur and serious noise. To tackle this problem, a novel model is proposed in this paper. Based on the original diffusion equation, we propose a new method for calculating the adaptive fidelity term and its coefficients, which is based on the relationship between the image gradient and the diffusion function. It is realized that the diffusion speed can be slowed down by adaptively changing the coefficient of the fidelity term, and it is proved mathematically that the proposed fractional adaptive fidelity term will not change the existence and uniqueness of the solution of the original model. At the same time, washout filter is introduced as the control item of the model, and a new model of image super-resolution reconstruction and image denoising is constructed. In the proposed model, the order of fractional differential will be determined adaptively by the local variance of the image. And we give the numerical calculation method of the new model in the frequency domain by the method of Fourier transform. The experimental results show that the proposed algorithm can better prevent the staircase effect and achieve better visual effect. And by introducing washout filter to act as the control of the model, the stability of the system can be improved and the system can converge to a stable state quickly.Jimin Yu Jiajun YinShangbo ZhouSaiao Huang Xianzhong Xie AIMS Pressarticleanisotropic diffusion equationadaptive gradient fidelity termwashout filterimage super-resolution reconstructionBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 6581-6607 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	anisotropic diffusion equation adaptive gradient fidelity term washout filter image super-resolution reconstruction Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	anisotropic diffusion equation adaptive gradient fidelity term washout filter image super-resolution reconstruction Biotechnology TP248.13-248.65 Mathematics QA1-939 Jimin Yu Jiajun Yin Shangbo Zhou Saiao Huang Xianzhong Xie An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation
description	The image denoising model based on anisotropic diffusion equation often appears the staircase effect while image denoising, and the traditional super-resolution reconstruction algorithm can not effectively suppress the noise in the image in the case of blur and serious noise. To tackle this problem, a novel model is proposed in this paper. Based on the original diffusion equation, we propose a new method for calculating the adaptive fidelity term and its coefficients, which is based on the relationship between the image gradient and the diffusion function. It is realized that the diffusion speed can be slowed down by adaptively changing the coefficient of the fidelity term, and it is proved mathematically that the proposed fractional adaptive fidelity term will not change the existence and uniqueness of the solution of the original model. At the same time, washout filter is introduced as the control item of the model, and a new model of image super-resolution reconstruction and image denoising is constructed. In the proposed model, the order of fractional differential will be determined adaptively by the local variance of the image. And we give the numerical calculation method of the new model in the frequency domain by the method of Fourier transform. The experimental results show that the proposed algorithm can better prevent the staircase effect and achieve better visual effect. And by introducing washout filter to act as the control of the model, the stability of the system can be improved and the system can converge to a stable state quickly.
format	article
author	Jimin Yu Jiajun Yin Shangbo Zhou Saiao Huang Xianzhong Xie
author_facet	Jimin Yu Jiajun Yin Shangbo Zhou Saiao Huang Xianzhong Xie
author_sort	Jimin Yu
title	An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation
title_short	An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation
title_full	An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation
title_fullStr	An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation
title_full_unstemmed	An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation
title_sort	image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/ad1ca843a6a24216861ae91118500353
work_keys_str_mv	AT jiminyu animagesuperresolutionreconstructionmodelbasedonfractionalorderanisotropicdiffusionequation AT jiajunyin animagesuperresolutionreconstructionmodelbasedonfractionalorderanisotropicdiffusionequation AT shangbozhou animagesuperresolutionreconstructionmodelbasedonfractionalorderanisotropicdiffusionequation AT saiaohuang animagesuperresolutionreconstructionmodelbasedonfractionalorderanisotropicdiffusionequation AT xianzhongxie animagesuperresolutionreconstructionmodelbasedonfractionalorderanisotropicdiffusionequation AT jiminyu imagesuperresolutionreconstructionmodelbasedonfractionalorderanisotropicdiffusionequation AT jiajunyin imagesuperresolutionreconstructionmodelbasedonfractionalorderanisotropicdiffusionequation AT shangbozhou imagesuperresolutionreconstructionmodelbasedonfractionalorderanisotropicdiffusionequation AT saiaohuang imagesuperresolutionreconstructionmodelbasedonfractionalorderanisotropicdiffusionequation AT xianzhongxie imagesuperresolutionreconstructionmodelbasedonfractionalorderanisotropicdiffusionequation
_version_	1718439615052906496

An image super-resolution reconstruction model based on fractional-order anisotropic diffusion equation

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