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An efficient non-convex total variation approach for image deblurring and denoising

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  • Liu, Jingjing
  • Ma, Ruijie
  • Zeng, Xiaoyang
  • Liu, Wanquan
  • Wang, Mingyu
  • Chen, Hui

Abstract

Total variation (TV) is broadly utilized in image processing because it is able to preserve sharp edges and object boundaries, which are usually the most important parts of an image. Recently, the non-convex functions such as the smoothly clipped absolute deviation, the minimax concave penalty, the capped ℓ1-norm penalty and the ℓp quasi-norm with 0

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  • 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).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300321000254
    DOI: 10.1016/j.amc.2021.125977
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    References listed on IDEAS

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    1. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
    2. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    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. 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).
    5. Xiu, Xianchao & Liu, Wanquan & Li, Ling & Kong, Lingchen, 2019. "Alternating direction method of multipliers for nonconvex fused regression problems," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 59-71.
    6. Xianchao Xiu & Lingchen Kong & Yan Li & Houduo Qi, 2018. "Iterative reweighted methods for $$\ell _1-\ell _p$$ ℓ 1 - ℓ p minimization," Computational Optimization and Applications, Springer, vol. 70(1), pages 201-219, May.
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    Cited by:

    1. Sining Huang & Yupeng Chen & Tiantian Qiao, 2021. "An Extended Reweighted ℓ 1 Minimization Algorithm for Image Restoration," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    2. Wang, Jian & Han, Ziwei & Jiang, Wenjing & Kim, Junseok, 2023. "A fast, efficient, and explicit phase-field model for 3D mesh denoising," Applied Mathematics and Computation, Elsevier, vol. 458(C).

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