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Fractional partial differential equation denoising models for texture image

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Abstract

In this paper, a set of fractional partial differential equations based on fractional total variation and fractional steepest descent approach are proposed to address the problem of traditional drawbacks of PM and ROF multi-scale denoising for texture image. By extending Green, Gauss, Stokes and Euler-Lagrange formulas to fractional field, we can find that the integer formulas are just their special case of fractional ones. In order to improve the denoising capability, we proposed 4 fractional partial differential equation based multiscale denoising models, and then discussed their stabilities and convergence rate. Theoretic deduction and experimental evaluation demonstrate the stability and astringency of fractional steepest descent approach, and fractional nonlinearly multi-scale denoising capability and best value of parameters are discussed also. The experiments results prove that the ability for preserving high-frequency edge and complex texture information of the proposed denoising models are obviously superior to traditional integral based algorithms, especially for texture detail rich images.

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Authors and Affiliations

  1. School of Computer Science and Technology, Sichuan University, Chengdu, 610065, China

    YiFei Pu, JiLiu Zhou & YiGuang Liu

  2. Université de Paris 12 (LiSSi, E.A. 3956), 61 av. du Général de Gaulle, 94010, CRETEIL Cedex, France

    Patrick Siarry

  3. Library of Sichuan University, Sichuan University, Chengdu, 610065, China

    Ni Zhang

  4. Computer Science College, Leshan Normal University, Leshan, 614000, China

    Guo Huang

  5. Wu Yuzhang Honors College of Sichuan University, Chengdu, 610065, China

    YiZhi Liu

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  1. YiFei Pu
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  4. YiGuang Liu
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Pu, Y., Siarry, P., Zhou, J. et al. Fractional partial differential equation denoising models for texture image. Sci. China Inf. Sci. 57, 1–19 (2014). https://doi.org/10.1007/s11432-014-5112-x

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