2012 Fiscal Year Final Research Report
Estimation of modeling errors and their regularization in applied inverse problems
| Project/Area Number |
23654034
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical 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) |
KUBO Masayoshi 京都大学, 情報学研究科, 講師 (10273616)
FUJIWARA Hiroshi 京都大学, 情報学研究科, 助教 (00362583)
OOISHI Naoya 京都大学, 医学(系)研究科(研究院), 研究員 (40526878)
IMAI Hitoshi 徳島大学, ソシオテクノサイエンス研究部, 教授 (80203298)
HIGASHIMORI Nobuyuki 一橋大学, 経済学研究科(研究院), 講 師 (10397573)
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| Project Period (FY) |
2011 – 2012
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| Keywords | 数学一般 / 応用数学 / 数値数学 / 数理モデル / 応用解析 / 数値解析 / 逆問題解析 / 光トモグラフィ |
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| Research Abstract |
We have obtained some new results as fundamental study for the diffused optical tomography (DOT), which is considered as a coming technology. The results are deduced through deep consideration, from both mathematics and computing, about mathematical models corresponding to DOT.In the project study, we focus on modeling errors which arise in mathematical modeling; we restrict ourselves to modeling errors in the transport equation model which is regarded as the fundamental mathematical one for propagation of photons in biomedical tissues. Through theoretical arguments and computings, we have pointed out some fatalmisunderstanding in the past studies for DOT based on mathematical analysis of the inverse problems.
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Research Products
(16 results)
