Multiplicative Noise Removal Based on the Smooth Diffusion Equation

Abstract

The multiplicative noise removal problem is of momentous significance in various image processing applications. In this paper, a nonlinear diffusion equation with smooth solution is proposed to remove multiplicative Gamma noise. The diffusion coefficient takes full advantage of two features of multiplicative noise image, namely, gradient information and gray level information, which makes the model has the ability to remove high level noise effectively and protect the edges. The existence of the solution has been analyzed by Schauder’s fixed-point theorem. Some other theoretical properties such as the maximum principle are also presented in the paper. In the numerical aspect, the explicit finite difference method, fast explicit diffusion method, additive operator splitting method and Krylov subspace spectral method are employed to implement the proposed model. Experimental results show that the fast explicit diffusion method achieves a better trade-off between computational time and denoising performance, and the Krylov subspace spectral method gets better restored results in the visual aspect. In addition, the capability of the proposed model for denoising is illustrated by comparison with other denoising models.

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Acknowledgements

The authors would like to thank the reviewers for the valuable suggestions to the paper and professor Patrick Guidotti from the University of California, Irvine, for sharing his code. This work is partially supported by the Natural Science Foundation of Heilongjiang Province of China (Grant Nos. LC2018001, A2016003), the National Science Foundation of China (Grant Nos. U1637208, 51476047), the Natural Science Foundation (Grant No. 11871133), the Fundamental Research Funds for the Central Universities and Program for Innovation Research of Science in Harbin Institute of Technology (PIRS OF HIT 201609), and the Fundamental Research Funds for the Central Universities and Program for Innovation Research of Science in Harbin Institute of Technology (PIRS OF HIT 201601).

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Shan, X., Sun, J. & Guo, Z. Multiplicative Noise Removal Based on the Smooth Diffusion Equation. J Math Imaging Vis 61, 763–779 (2019). https://doi.org/10.1007/s10851-018-00870-z

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Keywords

  • Multiplicative noise removal
  • Diffusion equation
  • Smooth solution
  • Fast algorithm