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An Extended Reweighted ℓ 1 Minimization Algorithm for Image Restoration

Author

Listed:
  • Sining Huang

    (Department of Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China)

  • Yupeng Chen

    (Department of Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China)

  • Tiantian Qiao

    (Department of Computational Mathematics, China University of Petroleum (East China), Qingdao 266580, China)

Abstract

This paper proposes an effective extended reweighted ℓ 1 minimization algorithm (ERMA) to solve the basis pursuit problem min u ∈ R n { | | u | | 1 : A u = f } in compressed sensing, where A ∈ R m × n , m ≪ n . The fast algorithm is based on linearized Bregman iteration with soft thresholding operator and generalized inverse iteration. At the same time, it also combines the iterative reweighted strategy that is used to solve min u ∈ R n { | | u | | p p : A u = f } problem, with the weight ω i ( u , p ) = ( ε + | u i | 2 ) p / 2 − 1 . Numerical experiments show that this ℓ 1 minimization persistently performs better than other methods. Especially when p = 0 , the restored signal by the algorithm has the highest signal to noise ratio. Additionally, this approach has no effect on workload or calculation time when matrix A is ill-conditioned.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3224-:d:701665
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    References listed on IDEAS

    as
    1. 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).
    2. 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.
    3. Cholamjiak, Watcharaporn & Dutta, Hemen & Yambangwai, Damrongsak, 2021. "Image restorations using an inertial parallel hybrid algorithm with Armijo linesearch for nonmonotone equilibrium problems," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
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