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Total variation with overlapping group sparsity for deblurring images under Cauchy noise

Author

Listed:
  • Ding, Meng
  • Huang, Ting-Zhu
  • Wang, Si
  • Mei, Jin-Jin
  • Zhao, Xi-Le

Abstract

The methods based on the total variation are effective for image deblurring and denoising, which can preserve edges and details of images. However, these methods usually produce some staircase effects. In order to alleviate the staircase effects, we propose a new convex model based on the total variation with overlapping group sparsity for recovering blurred images corrupted by Cauchy noise. Moreover, we develop an algorithm under the framework of the alternating direction method with multipliers, and use the majorization minimization to solve subproblems of the proposed algorithm. Numerical results illustrate that the proposed method outperforms other methods both in visual effects and quantitative measures, such as the peak signal-to-noise ratio and the structural similarity index.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:341:y:2019:i:c:p:128-147
    DOI: 10.1016/j.amc.2018.08.014
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    References listed on IDEAS

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    1. 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.
    2. Li, Fang & Lv, Xiaoguang, 2017. "A Decoupled method for image inpainting with patch-based low rank regulariztion," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 334-348.
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    Citations

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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. Ding, Meng & Huang, Ting-Zhu & Ma, Tian-Hui & Zhao, Xi-Le & Yang, Jing-Hua, 2020. "Cauchy noise removal using group-based low-rank prior," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    3. Jameel Ahmed Bhutto & Asad Khan & Ziaur Rahman, 2023. "Image Restoration with Fractional-Order Total Variation Regularization and Group Sparsity," Mathematics, MDPI, vol. 11(15), pages 1-23, July.
    4. Liu, Jingjing & Ma, Ruijie & Zeng, Xiaoyang & Liu, Wanquan & Wang, Mingyu & Chen, Hui, 2021. "An efficient non-convex total variation approach for image deblurring and denoising," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    5. Kuan Li & Chun Huang & Ziyang Yuan, 2021. "Error Estimations for Total Variation Type Regularization," Mathematics, MDPI, vol. 9(12), pages 1-14, June.

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