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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
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    References listed on IDEAS

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    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.
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