Image Reconstruction Algorithm Using Weighted Mean of Ordered-Subsets EM and MART for Computed Tomography

Omar M. Abou Al-Ola, Ryosuke Kasai, Yusaku Yamaguchi, Takeshi Kojima and Tetsuya Yoshinaga ()
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Omar M. Abou Al-Ola: Faculty of Science, Tanta University, El-Giesh St., Tanta 31527, Gharbia, Egypt
Ryosuke Kasai: Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan
Yusaku Yamaguchi: Shikoku Medical Center for Children and Adults, National Hospital Organization, 2-1-1 Senyu, Zentsuji 765-8507, Japan
Takeshi Kojima: Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan
Tetsuya Yoshinaga: Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan

Mathematics, 2022, vol. 10, issue 22, 1-17

Abstract: Iterative image reconstruction algorithms have considerable advantages over transform methods for computed tomography, but they each have their own drawbacks. In particular, the maximum-likelihood expectation-maximization (MLEM) algorithm reconstructs high-quality images even with noisy projection data, but it is slow. On the other hand, the simultaneous multiplicative algebraic reconstruction technique (SMART) converges faster at early iterations but is susceptible to noise. Here, we construct a novel algorithm that has the advantages of these different iterative schemes by combining ordered-subsets EM (OS-EM) and MART (OS-MART) with weighted geometric or hybrid means. It is theoretically shown that the objective function decreases with every iteration and the amount of decrease is greater than the mean between the decreases for OS-EM and OS-MART. We conducted image reconstruction experiments on simulated phantoms and deduced that our algorithm outperforms OS-EM and OS-MART alone. Our algorithm would be effective in practice since it incorporates OS-EM, which is currently the most popular technique of iterative image reconstruction from noisy measured projections.

Keywords: computed tomography; iterative reconstruction; ordered-subsets algorithm; maximum-likelihood expectation-maximization; multiplicative algebraic reconstruction technique (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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