2023 Fiscal Year Final Research Report
Mathematical and Numerical Analysis of Next-generation Imaging from Multiple Scattering Signals
| Project/Area Number |
20H01821
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
川越 大輔 京都大学, 情報学研究科, 助教 (30848073)
大石 直也 京都大学, 医学研究科, 特定准教授 (40526878)
吉川 仁 京都大学, 総合生存学館, 特定教授 (90359836)
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | 逆問題 / 数値解析 / 断層撮影法 / 多重散乱 / 輻射輸送方程式 / トモグラフィ |
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| Outline of Final Research Achievements |
One of the imaging modalities considered in this research project is diffuse optical tomography using near-infrared light for monitoring brain activity. We achieved a fast and reliable numerical method for light propagation in tissue with multiple scattering. In the numerical simulation, problems with approximately one billion degrees of freedom were processed, and the convergence of numerical solution with suitable norm was proved. We also proposed an imaging algorithm from near-infrared light, and showed its numerical realization. X-ray computerized tomography (CT) is also known as a practical imaging modalities, and mathematical algorithm of X-ray CT from local measurement was established. The algorithm is estimated with experimental measurement data, and its effectiveness was shown.
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| Free Research Field |
応用数学
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| Academic Significance and Societal Importance of the Research Achievements |
医用イメージングでの散乱信号の伝播は，輻射輸送方程式とよばれる数理モデルで表される．これは微分積分方程式であり，本研究では数値的取り扱い手法，得に数値シミュレーション結果の正しさを保証する方法と高速計算手法を確立した．また局所観測からのエックス線トモグラフィでは，約100年の間，研究開発の中心であった従来の積分方程式から，微分方程式へと数理モデルを転換して数値的手法を確立したことが大きな点である．
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