IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i23p4759-d1287389.html
   My bibliography  Save this article

Tomographic Reconstruction: General Approach to Fast Back-Projection Algorithms

Author

Listed:
  • Dmitry Polevoy

    (Federal Research Center Computer Science and Control RAS, 119333 Moscow, Russia
    Smart Engines Service LLC, 117312 Moscow, Russia)

  • Marat Gilmanov

    (Smart Engines Service LLC, 117312 Moscow, Russia
    Institute for Information Transmission Problems RAS, 127051 Moscow, Russia)

  • Danil Kazimirov

    (Smart Engines Service LLC, 117312 Moscow, Russia
    Institute for Information Transmission Problems RAS, 127051 Moscow, Russia)

  • Marina Chukalina

    (Smart Engines Service LLC, 117312 Moscow, Russia
    Institute for Information Transmission Problems RAS, 127051 Moscow, Russia)

  • Anastasia Ingacheva

    (Smart Engines Service LLC, 117312 Moscow, Russia
    Institute for Information Transmission Problems RAS, 127051 Moscow, Russia)

  • Petr Kulagin

    (Smart Engines Service LLC, 117312 Moscow, Russia
    Institute for Information Transmission Problems RAS, 127051 Moscow, Russia
    Phystech School of Applied Mathematics and Informatics, Moscow Institute of Physics and Technology (NRU), 141701 Dolgoprudny, Russia)

  • Dmitry Nikolaev

    (Smart Engines Service LLC, 117312 Moscow, Russia
    Institute for Information Transmission Problems RAS, 127051 Moscow, Russia)

Abstract

Addressing contemporary challenges in computed tomography (CT) demands precise and efficient reconstruction. This necessitates the optimization of CT methods, particularly by improving the algorithmic efficiency of the most computationally demanding operators—forward projection and backprojection. Every measurement setup requires a unique pair of these operators. While fast algorithms for calculating forward projection operators are adaptable across various setups, they fall short in three-dimensional scanning scenarios. Hence, fast algorithms are imperative for backprojection, an integral aspect of all established reconstruction methods. This paper introduces a general method for the calculation of backprojection operators in any measurement setup. It introduces a versatile method for transposing summation-based algorithms, which rely exclusively on addition operations. The proposed approach allows for the transformation of algorithms designed for forward projection calculation into those suitable for backprojection, with the latter maintaining asymptotic algorithmic complexity. Employing this method, fast algorithms for both forward projection and backprojection have been developed for the 2D few-view parallel-beam CT as well as for the 3D cone-beam CT. The theoretically substantiated complexity values for the proposed algorithms align with their experimentally derived estimates.

Suggested Citation

  • Dmitry Polevoy & Marat Gilmanov & Danil Kazimirov & Marina Chukalina & Anastasia Ingacheva & Petr Kulagin & Dmitry Nikolaev, 2023. "Tomographic Reconstruction: General Approach to Fast Back-Projection Algorithms," Mathematics, MDPI, vol. 11(23), pages 1-37, November.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4759-:d:1287389
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/23/4759/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/11/23/4759/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Anastasia S. Ingacheva & Marina V. Chukalina, 2019. "Polychromatic CT Data Improvement with One-Parameter Power Correction," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-12, April.
    Full references (including those not matched with items on IDEAS)

    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.

      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:gam:jmathe:v:11:y:2023:i:23:p:4759-:d:1287389. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.