IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/7932318.html
   My bibliography  Save this article

Tomographic Inverse Problem with Estimating Missing Projections

Author

Listed:
  • Masashi Kimura
  • Yusaku Yamaguchi
  • Omar M. Abou Al-Ola
  • Tetsuya Yoshinaga

Abstract

Image reconstruction in computed tomography can be treated as an inverse problem, namely, obtaining pixel values of a tomographic image from measured projections. However, a seriously degraded image with artifacts is produced when a certain part of the projections is inaccurate or missing. A novel method for simultaneously obtaining a reconstructed image and an estimated projection by solving an initial-value problem of differential equations is proposed. A system of differential equations is constructed on the basis of optimizing a cost function of unknown variables for an image and a projection. Three systems described by nonlinear differential equations are constructed, and the stability of a set of equilibria corresponding to an optimized solution for each system is proved by using the Lyapunov stability theorem. To validate the theoretical result given by the proposed method, metal artifact reduction was numerically performed.

Suggested Citation

  • Masashi Kimura & Yusaku Yamaguchi & Omar M. Abou Al-Ola & Tetsuya Yoshinaga, 2019. "Tomographic Inverse Problem with Estimating Missing Projections," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-11, March.
    • Handle: RePEc:hin:jnlmpe:7932318
    DOI: 10.1155/2019/7932318
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2019/7932318.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2019/7932318.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/7932318?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
    ---><---

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnlmpe:7932318. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.