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A fractional differential fidelity-based PDE model for image denoising

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Abstract

In this paper, a new partial differential equation (PDE)-based model is proposed for image denoising. The new method is inspired by previous works in which the nonlinear diffusion approach obtained by using a coupling gradient fidelity term. Based on the long-term memory and nonlocality of fractional differential, we introduce a new fidelity term based on the combination of fractional-order fidelity term and global fidelity term to measure the similarity in the variation of images, which can prevent the staircase effect, and simultaneously enhance the noisy image, thus, the image becomes clearer and brighter. Numerical results are presented in the end to demonstrate that with respect to image denoising capability, our fractional fidelity-based model outperforms the gradient fidelity-based model.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant No. 91630311), the Fundamental Research Funds for the Central Universities (Grant No. 2017XZZX007-02), and Zhejiang Provincial Natural Science Foundation of China (Grant No. LY15A010001).

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Qianting Ma & Dexing Kong

  2. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China

    Fangfang Dong

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  1. Qianting Ma
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  2. Fangfang Dong
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  3. Dexing Kong
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Correspondence to Dexing Kong.

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Ma, Q., Dong, F. & Kong, D. A fractional differential fidelity-based PDE model for image denoising. Machine Vision and Applications 28, 635–647 (2017). https://doi.org/10.1007/s00138-017-0857-z

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  • DOI: https://doi.org/10.1007/s00138-017-0857-z

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