IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v54y2013i2p317-342.html
   My bibliography  Save this article

Bregman operator splitting with variable stepsize for total variation image reconstruction

Author

Listed:
  • Yunmei Chen
  • William Hager
  • Maryam Yashtini
  • Xiaojing Ye
  • Hongchao Zhang

Abstract

This paper develops a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving problems of the form $\min\{\phi(Bu) +1/2\|Au-f\|_{2}^{2}\}$ , where ϕ may be nonsmooth. The original Bregman Operator Splitting (BOS) algorithm employed a fixed stepsize, while BOSVS uses a line search to achieve better efficiency. These schemes are applicable to total variation (TV)-based image reconstruction. The stepsize rule starts with a Barzilai-Borwein (BB) step, and increases the nominal step until a termination condition is satisfied. The stepsize rule is related to the scheme used in SpaRSA (Sparse Reconstruction by Separable Approximation). Global convergence of the proposed BOSVS algorithm to a solution of the optimization problem is established. BOSVS is compared with other operator splitting schemes using partially parallel magnetic resonance image reconstruction problems. The experimental results indicate that the proposed BOSVS algorithm is more efficient than the BOS algorithm and another split Bregman Barzilai-Borwein algorithm known as SBB. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Yunmei Chen & William Hager & Maryam Yashtini & Xiaojing Ye & Hongchao Zhang, 2013. "Bregman operator splitting with variable stepsize for total variation image reconstruction," Computational Optimization and Applications, Springer, vol. 54(2), pages 317-342, March.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:2:p:317-342
    DOI: 10.1007/s10589-012-9519-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-012-9519-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-012-9519-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mingqiang Zhu & Stephen Wright & Tony Chan, 2010. "Duality-based algorithms for total-variation-regularized image restoration," Computational Optimization and Applications, Springer, vol. 47(3), pages 377-400, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Maryam Yashtini, 2022. "Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 913-939, December.
    2. William W. Hager & Hongchao Zhang, 2019. "Inexact alternating direction methods of multipliers for separable convex optimization," Computational Optimization and Applications, Springer, vol. 73(1), pages 201-235, May.
    3. William W. Hager & Hongchao Zhang, 2020. "Convergence rates for an inexact ADMM applied to separable convex optimization," Computational Optimization and Applications, Springer, vol. 77(3), pages 729-754, December.
    4. Maryam Yashtini, 2021. "Multi-block Nonconvex Nonsmooth Proximal ADMM: Convergence and Rates Under Kurdyka–Łojasiewicz Property," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 966-998, September.
    5. Jianchao Bai & William W. Hager & Hongchao Zhang, 2022. "An inexact accelerated stochastic ADMM for separable convex optimization," Computational Optimization and Applications, Springer, vol. 81(2), pages 479-518, March.

    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. Pengwen Chen & Changfeng Gui, 2013. "Linear convergence analysis of the use of gradient projection methods on total variation problems," Computational Optimization and Applications, Springer, vol. 54(2), pages 283-315, March.

    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:spr:coopap:v:54:y:2013:i:2:p:317-342. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.