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Semi-blind image deblurring by a proximal alternating minimization method with convergence guarantees

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  • Dou, Hong-Xia
  • Huang, Ting-Zhu
  • Zhao, Xi-Le
  • Huang, Jie
  • Liu, Jun

Abstract

The semi-blind image deblurring problem aims to simultaneously estimate the clean image and the point spread function (PSF), which results in a (jointly) nonconvex optimization problem. In this paper, we develop an efficient algorithm to tackle the corresponding minimization problem based on the framework of the proximal alternating minimization (PAM). We also establish the convergence of the proposed algorithm under a mild assumption. Numerical experiments demonstrate our approach could obtain a more robust performance than the related state-of-the-art semi-blind image deblurring method.

Suggested Citation

  • Dou, Hong-Xia & Huang, Ting-Zhu & Zhao, Xi-Le & Huang, Jie & Liu, Jun, 2020. "Semi-blind image deblurring by a proximal alternating minimization method with convergence guarantees," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    • Handle: RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320301375
    DOI: 10.1016/j.amc.2020.125168
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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. Jinming Duan & Zhenkuan Pan & Baochang Zhang & Wanquan Liu & Xue-Cheng Tai, 2015. "Fast algorithm for color texture image inpainting using the non-local CTV model," Journal of Global Optimization, Springer, vol. 62(4), pages 853-876, August.
    3. Saha, Tanay & Srivastava, Shwetabh & Khare, Swanand & Stanimirović, Predrag S. & Petković, Marko D., 2019. "An improved algorithm for basis pursuit problem and its applications," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 385-398.
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