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ID 113352
タイトル別表記
コンピュータ断層のための加速化OS-EMアルゴリズムに対応した連続時間系
著者
立石, 貴代子 徳島大学大学院保健科学教育部(保健学専攻)
山口, 雄作 Shikoku Medical Center for Children and Adults
Abou Al-Ola, Omar M. Tanta University
キーワード
Computed tomography
Image reconstruction
Inverse problem
Iterative reconstruction
Dynamical system
資料タイプ
学位論文
抄録
The maximum-likelihood expectation-maximization (ML-EM) algorithm is used for an iterative image reconstruction (IIR) method and performs well with respect to the inverse problem as cross-entropy minimization in computed tomography. For accelerating the convergence rate of the ML-EM, the ordered-subsets expectation-maximization (OS-EM) with a power factor is effective. In this paper, we propose a continuous analog to the power-based accelerated OS-EM algorithm. The continuous-time image reconstruction (CIR) system is described by nonlinear differential equations with piecewise smooth vector fields by a cyclic switching process. A numerical discretization of the differential equation by using the geometric multiplicative first-order expansion of the nonlinear vector field leads to an exact equivalent iterative formula of the power-based OS-EM. The convergence of nonnegatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem for consistent inverse problems. We illustrate through numerical experiments that the convergence characteristics of the continuous system have the highest quality compared with that of discretization methods. We clarify how important the discretization method approximates the solution of the CIR to design a better IIR method.
掲載誌名
Mathematical Problems in Engineering
ISSN
1024123X
15635147
cat書誌ID
AA11947206
出版者
Hindawi
2017
開始ページ
1564123
発行日
2017-08-06
備考
内容要旨・審査要旨・論文本文の公開
本論文は,著者Kiyoko Tateishiの学位論文として提出され,学位審査・授与の対象となっている。
権利情報
© 2017 Kiyoko Tateishi et al. This is an open access article distributed under the Creative Commons Attribution License ( https://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
EDB ID
出版社版DOI
出版社版URL
フルテキストファイル
言語
eng
著者版フラグ
博士論文全文を含む
文科省報告番号
甲第3272号
学位記番号
甲保第37号
学位授与年月日
2019-03-20
学位名
博士(保健学)
学位授与機関
徳島大学
部局
医学系