A NON-LOCAL DIFFUSION EQUATION FOR NOISE REMOVAL

doi:10.1007/s10473-022-0505-1

Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (5): 1779-1808.doi: 10.1007/s10473-022-0505-1

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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).

Abstract

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

CLC Number:

35K59

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

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