Extended Ordered-subsets Expectation-maximization Algorithm with Power Exponent for Noise-robust Image Reconstruction in Computed Tomography

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  • Yamaguchi Yusaku
    National Hospital Organization, Shikoku Medical Center for Children and Adults, 2-1-1 Senyu, Zentsuji, Kagawa 765-8507, Japan
  • Kudo Moe
    Graduate School of Health Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan
  • Kojima Takeshi
    Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan
  • Al-Ola Omar Mohammad Abou
    Faculty of Science, Tanta University, El-Giesh St., Tanta, Gharbia 31527, Egypt
  • Yoshinaga Tetsuya
    Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan

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<p>The maximum-likelihood expectation-maximization (ML-EM) algorithm is the most popular iterative reconstruction method in emission-computed tomography with a noise model based on the Poisson distribution. The ordered-subsets EM (OS-EM) algorithm is known owing to accelerating the convergence of the ML-EM algorithm with the drawback of slow convergence. In this paper, we propose an extended OS-EM algorithm with a power exponent. We theoretically prove the asymptotic stability of an equilibrium corresponding to the solution of the nonlinear hybrid dynamical system whose numerical discretization based on multiplicative calculus coincides with the extended OS-EM algorithm. We provide a numerical experiment to demonstrate the effectiveness of the proposed system and confirm the acceleration of the proposed method and the robustness against noise. The reconstruction of high-quality images made by the method even when the projection data is noisy allows patient dose reduction in clinical practice.</p>

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