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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Omar M. Abou Al-Ola & Ryosuke Kasai & Yusaku Yamaguchi & Takeshi Kojima & Tetsuya Yoshinaga, 2022. "Image Reconstruction Algorithm Using Weighted Mean of Ordered-Subsets EM and MART for Computed Tomography," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4277-:d:973727
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    References listed on IDEAS

    as
    1. Kiyoko Tateishi & Yusaku Yamaguchi & Omar M. Abou Al-Ola & Tetsuya Yoshinaga, 2017. "Continuous Analog of Accelerated OS-EM Algorithm for Computed Tomography," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, August.
    2. Omar M. Abou Al-Ola & Ken'ichi Fujimoto & Tetsuya Yoshinaga, 2011. "Common Lyapunov Function Based on Kullback–Leibler Divergence for a Switched Nonlinear System," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-12, May.
    3. Wenbo Jiang & Xiaohua Zhang, 2017. "Relaxation Factor Optimization for Common Iterative Algorithms in Optical Computed Tomography," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, July.
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