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Fractional-order total variation image denoising based on proximity algorithm

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  • Chen, Dali
  • Chen, YangQuan
  • Xue, Dingyu

Abstract

The fractional-order total variation(TV) image denoising model has been proved to be able to avoid the “blocky effect”. However, it is difficult to be solved due to the non-differentiability of the fractional-order TV regularization term. In this paper, the proximity algorithm is used to solve the fractional-order TV optimization problem, which provides an effective tool for the study of the fractional-order TV denoising model. In this method, the complex fractional-order TV optimization problem is solved by using a sequence of simpler proximity operators, and therefore it is effective to deal with the problem of algorithm implementation. The final numerical procedure is given for image denoising, and the experimental results verify the effectiveness of the algorithm.

Suggested Citation

  • Chen, Dali & Chen, YangQuan & Xue, Dingyu, 2015. "Fractional-order total variation image denoising based on proximity algorithm," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 537-545.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:537-545
    DOI: 10.1016/j.amc.2015.01.012
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    Cited by:

    1. Yang, Jing-Hua & Zhao, Xi-Le & Ji, Teng-Yu & Ma, Tian-Hui & Huang, Ting-Zhu, 2020. "Low-rank tensor train for tensor robust principal component analysis," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Zeshan Aslam Khan & Naveed Ishtiaq Chaudhary & Syed Zubair, 2019. "Fractional stochastic gradient descent for recommender systems," Electronic Markets, Springer;IIM University of St. Gallen, vol. 29(2), pages 275-285, June.
    3. Ding, Meng & Huang, Ting-Zhu & Wang, Si & Mei, Jin-Jin & Zhao, Xi-Le, 2019. "Total variation with overlapping group sparsity for deblurring images under Cauchy noise," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 128-147.
    4. Boutaayamou, Idriss & Hadri, Aissam & Laghrib, Amine, 2023. "An optimal bilevel optimization model for the generalized total variation and anisotropic tensor parameters selection," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    5. Tang Ruiyin & Liu Bo, 2023. "Application of Fractional Differential Model in Image Enhancement of Strong Reflection Surface," Mathematics, MDPI, vol. 11(2), pages 1-16, January.
    6. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.

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