Tomographic Inverse Problem with Estimating Missing Projections

• Material Type: 博士論文
• Title: Tomographic Inverse Problem with Estimating Missing Projections
• Author/Editor: Kimura, Masashi; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Yoshinaga, Tetsuya
• Author Heading: Kimura, Masashi; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Yoshinaga, Tetsuya
• Publication, Distribution, etc.: Hindawi
• Publication Date: 2019-03-13
• Publication Date (W3CDTF): 2019-03-13
• Alternative Title: 欠損した投影の推定を伴う断層逆問題
• Periodical title: Mathematical Problems in Engineering
• No. or year of volume/issue: 2019
• Volume: 2019
• Pages: 7932318-
• ISSN (Periodical Title): ISSN : 1024-123X; ISSN : 1563-5147
• Degree grantor/type: 徳島大学
• Date Granted: 2020-03-23
• Dissertation Number: 甲第3422号
• Degree Type: 博士（保健学）
• Text Language Code: eng
• Subject Heading: Inverse Problem; Nonlinear Dynamical System; Image Reconstruction; Metal Artifact Reduction
• Target Audience: 一般
• Note (General): Image reconstruction in computed tomography can be treated as an inverse problem, namely, obtaining pixel values of a tomographic image from measured projections. However, a seriously degraded image with artifacts is produced when a certain part of the projections is inaccurate or missing. A novel method for simultaneously obtaining a reconstructed image and an estimated projection by solving an initial-value problem of differential equations is proposed. A system of differential equations is constructed on the basis of optimizing a cost function of unknown variables for an image and a projection. Three systems described by nonlinear differential equations are constructed, and the stability of a set of equilibria corresponding to an optimized solution for each system is proved by using the Lyapunov stability theorem. To validate the theoretical result given by the proposed method, metal artifact reduction was numerically performed.
• Format (IMT): application/pdf
• Access Restrictions: インターネット公開
• Rights (production): Copyright © 2019 Masashi Kimura 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.
• Related Material (DOI): 10.1155/2019/7932318
• Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）; https://irdb.nii.ac.jp
• Original Data Provider (Database): 徳島大学 : 徳島大学機関リポジトリ

Table of Contents

https://repo.lib.tokushima-u.ac.jp/files/public/11/114384/20200514170153429715/k3422_abstract.pdf fulltext

https://repo.lib.tokushima-u.ac.jp/files/public/11/114384/20200514170154140687/k3422_review.pdf fulltext

https://repo.lib.tokushima-u.ac.jp/files/public/11/114384/20200514170154859074/k3422_fulltext.pdf fulltext