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A gray level indicator-based nonlinear diffusion equation for the removal of random-valued impulse noise

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Abstract

This paper proposes a nonlinear diffusion equation with two diffusivities to restore images corrupted by random-valued impulse noise. A Perona–Malik type diffusivity is utilized for anisotropic diffusion and a gray level based diffusivity called gray level indicator is proposed to estimate the amplitude of the noise. Then the proposed equation has a large diffusion coefficient for homogeneous regions and regions corrupted by large impulse noise. Conversely, it has a small diffusion coefficient for regions with edges, fine details, as well as regions corrupted by small impulse noise. The gray level indicator is constructed as the square of the difference between the noisy image and a reference image deduced from median-type filters. The new equation is able to remove small random-valued impulse noise that is difficult to be detected. A robust stopping criteria based on the complexity of the restored image and the noise level is proposed. Numerical experiments show that it outperforms PDE-based methods and nonlocal methods.

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Acknowledgements

The authors would like to thank Ming Yan for sharing his code of AOP with us and thank Yang Chen for sharing his code of SAFE with us. The author would also like to thank the referees for the valuable suggestions and comments. This work was supported by the National Natural Science Foundation of China (12001509) and the Natural Science Foundation of Zhejiang Province (LQ21A010010).

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  1. Department of Mathematics, China Jiliang University, Hangzhou, 310018, China

    Kehan Shi

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Shi, K. A gray level indicator-based nonlinear diffusion equation for the removal of random-valued impulse noise. Multimed Tools Appl 81, 10529–10544 (2022). https://doi.org/10.1007/s11042-022-12255-x

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