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.
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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).
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Shao, J., Guo, Z., Yao, W. et al. A Non-Local Diffusion Equation for Noise Removal. Acta Math Sci 42, 1779–1808 (2022). https://doi.org/10.1007/s10473-022-0505-1
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DOI: https://doi.org/10.1007/s10473-022-0505-1