IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v29y2021i05ns0218348x21501255.html
   My bibliography  Save this article

A Nonlocal Low-Rank Regularization Method For Fractal Image Coding

Author

Listed:
  • YURU ZOU

    (Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China)

  • HUAXUAN HU

    (Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China)

  • JIAN LU

    (Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China)

  • XIAOXIA LIU

    (Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, P. R. China)

  • QINGTANG JIANG

    (Department of Mathematics and Statistics, University of Missouri-St. Louis, St. Louis, MO 63121, USA)

  • GUOHUI SONG

    (Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA)

Abstract

Fractal coding has been widely used as an image compression technique in many image processing problems in the past few decades. On the other hand side, most of the natural images have the characteristic of nonlocal self-similarity that motivates low-rank representations of them. We would employ both the fractal image coding and the nonlocal self-similarity priors to achieve image compression in image denoising problems. Specifically, we propose a new image denoising model consisting of three terms: a patch-based nonlocal low-rank prior, a data-fidelity term describing the closeness of the underlying image to the given noisy image, and a quadratic term measuring the closeness of the underlying image to a fractal image. Numerical results demonstrate the superior performance of the proposed model in terms of peak-signal-to-noise ratio, structural similarity index and mean absolute error.

Suggested Citation

  • Yuru Zou & Huaxuan Hu & Jian Lu & Xiaoxia Liu & Qingtang Jiang & Guohui Song, 2021. "A Nonlocal Low-Rank Regularization Method For Fractal Image Coding," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-14, August.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x21501255
    DOI: 10.1142/S0218348X21501255
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X21501255
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X21501255?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.

    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:wsi:fracta:v:29:y:2021:i:05:n:s0218348x21501255. 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: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/fractals .

    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.