Fast algorithm for Joseph’s forward projection in iterative computed tomography reconstruction

Zhang, Shunli; Zhang, Yingze; Tuo, Mingxiu; Zhang, Haibo

doi:10.1007/s12652-022-04324-8

Cited by 1 publication

(1 citation statement)

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“…Streamlining this process holds great promise for speeding up the entire reconstruction process. The acceleration of classical algorithms of CT reconstruction is an on-going problem with main efforts being directed towards effective GPU implementations [31,32], although new fast algorithms are being developed as well [33,34]. There are fast algorithms for calculating the forward projection operator for various tomographic setups.…”

Section: Introduction 1problem Relevancementioning

confidence: 99%

Tomographic Reconstruction: General Approach to Fast Back-Projection Algorithms

Polevoy,

Gilmanov,

Kazimirov

et al. 2023

Mathematics

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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.

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