Continuous Analog of Accelerated OS-EM Algorithm for Computed Tomography

• Material Type: 博士論文
• ISSN: 1024-123X
• Title: Continuous Analog of Accelerated OS-EM Algorithm for Computed Tomography
• Volume: 2017
• Author/Editor: Tateishi, Kiyoko; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Yoshinaga, Tetsuya
• Author Heading: Tateishi, Kiyoko; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Yoshinaga, Tetsuya
• Publication, Distribution, etc.: Hindawi
• Publication Date: 2017-08-06
• Publication Date (W3CDTF): 2017-08-06
• Alternative Title: 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
• Periodical title: Mathematical Problems in Engineering
• Degree grantor/type: 徳島大学
• Date Granted: 2019-03-20
• Date Granted (W3CDTF): 2019-03-20
• Dissertation Number: 甲第3272号
• Degree Type: 博士（保健学）
• Conferring No. (Dissertation): 甲第3272号
• Text Language Code: eng
• Subject Heading: Computed tomography; Image reconstruction; Inverse problem; Iterative reconstruction; Dynamical system
• Target Audience: 一般
• Note (General): 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.
• DOI: info:doi/10.1155/2017/1564123; https://doi.org/info:doi/10.1155/2017/1564123
• Persistent ID (NDL): info:ndljp/pid/11300296; https://dl.ndl.go.jp/pid/11300296
• Collection: 障害者向け資料
• Collection (Materials For Handicapped People:1): テキストデータ
• Collection (particular): 国立国会図書館デジタルコレクション > デジタル化資料 > 博士論文; https://dl.ndl.go.jp/collections/A00014
• Acquisition Basis: 博士論文（自動収集）
• Date Accepted (W3CDTF): 2019-07-05T01:13:02+09:00
• Format (IMT): application/pdf
• Access Restrictions: 国立国会図書館内限定公開
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• Availability of remote photoduplication service: 可
• Periodical Title (URI): http://repo.lib.tokushima-u.ac.jp/113352
• Data Provider (Database): 国立国会図書館 : 国立国会図書館デジタルコレクション; https://dl.ndl.go.jp