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.
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
.
DOI: 10.1007/s10473-022-0505-1
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