IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v355y2019icp385-398.html
   My bibliography  Save this article

An improved algorithm for basis pursuit problem and its applications

Author

Listed:
  • Saha, Tanay
  • Srivastava, Shwetabh
  • Khare, Swanand
  • Stanimirović, Predrag S.
  • Petković, Marko D.

Abstract

We propose an algorithm for solving the basis pursuit problem minu∈Cn{∥u∥1:Au=f}. Our starting motivation is the algorithm for compressed sensing, proposed by Qiao, Li and Wu, which is based on linearized Bregman iteration with generalized inverse. Qiao, Li and Wu defined new algorithm for solving the basis pursuit problem in compressive sensing using a linearized Bregman iteration and the iterative formula of linear convergence for computing the matrix generalized inverse. In our proposed approach, we combine a partial application of the Newton’s second order iterative scheme for computing the generalized inverse with the Bregman iteration. Our scheme takes lesser computational time and gives more accurate results in most cases. The effectiveness of the proposed scheme is illustrated in two applications: signal recovery from noisy data and image deblurring.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:385-398
    DOI: 10.1016/j.amc.2019.02.073
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319301833
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.02.073?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.

    Citations

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


    Cited by:

    1. Vincenzo Bonifaci, 2021. "A Laplacian approach to $$\ell _1$$ ℓ 1 -norm minimization," Computational Optimization and Applications, Springer, vol. 79(2), pages 441-469, June.
    2. 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).

    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:eee:apmaco:v:355:y:2019:i:c:p:385-398. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.