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Alternating split Bregman method for the bilaterally constrained image deblurring problem

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  • Shi, Baoli
  • Pang, Zhi-Feng
  • Wu, Jun

Abstract

This paper studies the image deblurring problem based on a bilateral constraint by convexly combining two classes of total-variation-type functionals. The proposed model including two L1-norm terms leads to some numerical difficulties, so we employ the alternating split Bregman method (ASB) to solve it which can be reinterpreted as Douglas–Rachford splitting applied to the dual problem. We also prove that the alternating split Bregman method owns the convergence rate O1M for the iteration M. Experimental results demonstrate the viability and efficiency of the proposed model and algorithm to restore blurring and noisy images.

Suggested Citation

  • Shi, Baoli & Pang, Zhi-Feng & Wu, Jun, 2015. "Alternating split Bregman method for the bilaterally constrained image deblurring problem," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 402-414.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:402-414
    DOI: 10.1016/j.amc.2014.11.004
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    1. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
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    Cited by:

    1. Lv, Xiao-Guang & Jiang, Le & Liu, Jun, 2016. "Deblurring Poisson noisy images by total variation with overlapping group sparsity," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 132-148.
    2. Wu, Tingting & Shao, Jinbo & Gu, Xiaoyu & Ng, Michael K. & Zeng, Tieyong, 2021. "Two-stage image segmentation based on nonconvex ℓ2−ℓp approximation and thresholding," Applied Mathematics and Computation, Elsevier, vol. 403(C).

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