A NON-LOCAL DIFFUSION EQUATION FOR NOISE REMOVAL

doi:10.1007/s10473-022-0505-1

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (5): 1779-1808.doi: 10.1007/s10473-022-0505-1

• 论文 • 上一篇

A NON-LOCAL DIFFUSION EQUATION FOR NOISE REMOVAL

Jingfeng SHAO¹, Zhichang GUO¹, Wenjuan YAO¹, Dong YAN², Boying WU¹

1. School of Mathematics, Harbin Institute of Technology, Harbin, 15000, China;
2. School of Mathematics, University of California at Irvine, Irvine, 92697, U. S. A.

收稿日期:2021-03-26 修回日期:2022-05-18 发布日期:2022-11-02
通讯作者: Boying Wu,E-mail:mathwby@hit.edu.cn E-mail:mathwby@hit.edu.cn
基金资助:
This work was partially supported by the National Natural Science Foundation of China (11971131, 12171123, 11871133, 11671111, U1637208, 61873071, 51476047), the Guangdong Basic and Applied Basic Research Foundation (2020B1515310006), and the Natural Sciences Foundation of Heilongjiang Province (LH2021A011) and China Postdoctoral Science Foundation (2020M670893).

A NON-LOCAL DIFFUSION EQUATION FOR NOISE REMOVAL

Jingfeng SHAO¹, Zhichang GUO¹, Wenjuan YAO¹, Dong YAN², Boying WU¹

1. School of Mathematics, Harbin Institute of Technology, Harbin, 15000, China;
2. School of Mathematics, University of California at Irvine, Irvine, 92697, U. S. A.

Received:2021-03-26 Revised:2022-05-18 Published:2022-11-02
Contact: Boying Wu,E-mail:mathwby@hit.edu.cn E-mail:mathwby@hit.edu.cn
Supported by:
This work was partially supported by the National Natural Science Foundation of China (11971131, 12171123, 11871133, 11671111, U1637208, 61873071, 51476047), the Guangdong Basic and Applied Basic Research Foundation (2020B1515310006), and the Natural Sciences Foundation of Heilongjiang Province (LH2021A011) and China Postdoctoral Science Foundation (2020M670893).

摘要/Abstract

摘要： In this paper, we propose a new non-local diffusion equation for noise removal, which is derived from the classical Perona-Malik equation (PM equation) and the regularized PM equation. Using the convolution of the image gradient and the gradient, we propose a new diffusion coefficient. Due to the use of the convolution, the diffusion coefficient is non-local. However, the solution of the new diffusion equation may be discontinuous and belong to the bounded variation space (BV space). By virtue of Young measure method, the existence of a BV solution to the new non-local diffusion equation is established. Experimental results illustrate that the new method has some non-local performance and performs better than the original PM and other methods.

关键词: image denoising, non-local diffusion, BV solutions, Perona-Malik method

Abstract: In this paper, we propose a new non-local diffusion equation for noise removal, which is derived from the classical Perona-Malik equation (PM equation) and the regularized PM equation. Using the convolution of the image gradient and the gradient, we propose a new diffusion coefficient. Due to the use of the convolution, the diffusion coefficient is non-local. However, the solution of the new diffusion equation may be discontinuous and belong to the bounded variation space (BV space). By virtue of Young measure method, the existence of a BV solution to the new non-local diffusion equation is established. Experimental results illustrate that the new method has some non-local performance and performs better than the original PM and other methods.

Key words: image denoising, non-local diffusion, BV solutions, Perona-Malik method

中图分类号:

35K59

Jingfeng SHAO, Zhichang GUO, Wenjuan YAO, Dong YAN, Boying WU. A NON-LOCAL DIFFUSION EQUATION FOR NOISE REMOVAL[J]. 数学物理学报(英文版), 2022, 42(5): 1779-1808.

Jingfeng SHAO, Zhichang GUO, Wenjuan YAO, Dong YAN, Boying WU. A NON-LOCAL DIFFUSION EQUATION FOR NOISE REMOVAL[J]. Acta mathematica scientia,Series B, 2022, 42(5): 1779-1808.

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A NON-LOCAL DIFFUSION EQUATION FOR NOISE REMOVAL

A NON-LOCAL DIFFUSION EQUATION FOR NOISE REMOVAL

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