2016 Fiscal Year Final Research Report
Fundamental study for high-resolution diffused optical tomography based on numerical analysis and applied analysis
| Project/Area Number |
25287028
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kyoto University |
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Principal Investigator |
Iso Yuusuke 京都大学, 情報学研究科, 教授 (70203065)
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| Co-Investigator(Kenkyū-buntansha) |
藤原 宏志 京都大学, 情報学研究科, 准教授 (00362583)
久保 雅義 京都大学, 情報学研究科, 講師 (10273616)
山田 幸生 電気通信大学, 学内共同利用施設等, 教授 (10334583)
大石 直也 京都大学, 医学(系)研究科(研究院), 助教 (40526878)
今井 仁司 同志社大学, 理工学部, 教授 (80203298)
東森 信就 一橋大学, 経済学研究科(研究院), その他 (10397573)
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| Co-Investigator(Renkei-kenkyūsha) |
FUKUYAMA Hidenao 京都大学, 大学院医学研究科, 教授 (90181297)
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| Research Collaborator |
NISHIDA Takaaki 京都大学, 名誉教授
YAMAMOTO Masahiro 東京大学, 教授
LIU Tai-Ping 台湾中央研究院, 数学研究所
Dmitri Anikonov ロシア科学アカデミーSobolev, 数学研究所
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | 応用数学 / 数理モデル / 数値数学 / 光トモグラフィ / 大規模数値計算 / 微分方程式 / 逆問題解析 |
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| Outline of Final Research Achievements |
This project is aimed at innovation of the diffused optical tomography(DOT) from the view point of mathematical science, and DOT is consideredas an inverse problem to detect unknown coefficients in the radiative transport equation (RTE). There are two approaches to the inverse problem;the one is based on time resolution data as observation, and the other is based on stationary data. We obtained prominent result for the former case,and we focus on discontinuity of the coefficients as to show nice images numerically through reconstruction of the coefficients having discontinuity.We also prove convergence of the CIP (Cubic Interpolation Pseudoparticle) method to solve hyperbolic partial differential equations, which is used in our numerical simulation, to give an affirmative answer to an open problem about the CIP scheme. We propose new idea on iteration approach to the latter case, and we show new effective algorithm for numerical
simulation of the stationary RTE.
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| Free Research Field |
応用数学
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