IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i24p3224-d701665.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/24/3224/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/24/3224/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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).
    2. 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).
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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).
    3. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3224-:d:701665. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.