IDEAS home Printed from https://ideas.repec.org/h/spr/spochp/978-3-030-72563-1_17.html
   My bibliography  Save this book chapter

Piecewise Polynomial Inversion of the Radon Transform in Three Space Dimensions via Plane Integration and Applications in Positron Emission Tomography

In: Nonlinear Analysis, Differential Equations, and Applications

Author

Listed:
  • Nicholas E. Protonotarios

    (University of Cambridge
    Academy of Athens)

  • George A. Kastis

    (Academy of Athens)

  • Nikolaos Dikaios

    (Academy of Athens)

  • Athanassios S. Fokas

    (University of Cambridge
    Academy of Athens
    University of Southern California)

Abstract

The inversion of the celebrated Radon transform in three dimensions involves two-dimensional plane integration. This inversion provides the mathematical foundation of the important field of medical imaging, known as three-dimensional positron emission tomography (3D PET). In this chapter, we present an analytical expression for the inversion of the three-dimensional Radon transform, as well as a novel numerical implementation of this formula, based on piecewise polynomials of the third degree.

Suggested Citation

  • Nicholas E. Protonotarios & George A. Kastis & Nikolaos Dikaios & Athanassios S. Fokas, 2021. "Piecewise Polynomial Inversion of the Radon Transform in Three Space Dimensions via Plane Integration and Applications in Positron Emission Tomography," Springer Optimization and Its Applications, in: Themistocles M. Rassias (ed.), Nonlinear Analysis, Differential Equations, and Applications, pages 381-396, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-72563-1_17
    DOI: 10.1007/978-3-030-72563-1_17
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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:spr:spochp:978-3-030-72563-1_17. 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: 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.