Tomographic Reconstruction: General Approach to Fast Back-Projection Algorithms

Dmitry Polevoy, Marat Gilmanov, Danil Kazimirov (), Marina Chukalina (), Anastasia Ingacheva, Petr Kulagin and Dmitry Nikolaev
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Dmitry Polevoy: Federal Research Center Computer Science and Control RAS, 119333 Moscow, Russia
Marat Gilmanov: Smart Engines Service LLC, 117312 Moscow, Russia
Danil Kazimirov: Smart Engines Service LLC, 117312 Moscow, Russia
Marina Chukalina: Smart Engines Service LLC, 117312 Moscow, Russia
Anastasia Ingacheva: Smart Engines Service LLC, 117312 Moscow, Russia
Petr Kulagin: Smart Engines Service LLC, 117312 Moscow, Russia
Dmitry Nikolaev: Smart Engines Service LLC, 117312 Moscow, Russia

Mathematics, 2023, vol. 11, issue 23, 1-37

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.

Keywords: fast Hough transform; fast discrete radon transform; computed tomography (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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