A NON-LOCAL DIFFUSION EQUATION FOR NOISE REMOVAL

作     者：Jingfeng SHAO Zhichang GUO Wenjuan YAO Dong YAN Boying WU 邵景峰;郭志昌;姚文娟;严冬;吴勃英

作者机构：School of MathematicsHarbin Institute of TechnologyHarbin 15000China School of MathematicsUniversity of California at IrvineIrvine 92697U.S.A. 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2022年第42卷第5期

页      面：1779-1808页

核心收录：

学科分类：07[理学] 08[工学] 080203[工学-机械设计及理论] 070104[理学-应用数学] 0802[工学-机械工程] 0701[理学-数学] 

基　　金：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) the Natural Sciences Foundation of Heilongjiang Province(LH2021A011) China Postdoctoral Science Foundation(2020M670893) 

主　　题：image denoising non-local diffusion BV solutions Perona-Malik method 

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 *** the convolution of the image gradient and the gradient,we propose a new diffusion *** to the use of the convolution,the diffusion coefficient is ***,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 *** results illustrate that the new method has some non-local performance and performs better than the original PM and other methods.