1997 Fiscal Year Final Research Report Summary
Linear algebraic methods of image reconstruction and their applications to plasma measurements.
| Project/Area Number |
08680511
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
プラズマ理工学
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| Research Institution | Toyama Kenritu University |
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Principal Investigator |
IWAMA Naofumi Toyama Kenritsu University, Department of Electronics and Informatics, Professor, 工学部, 教授 (30023253)
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| Co-Investigator(Kenkyū-buntansha) |
HOSODA Yohsuke Toyama Kenritsu University, Department of Electronics and Informatics, Research, 工学部, 助手 (80264951)
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| Project Period (FY) |
1996 – 1997
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| Keywords | plasma measurement / image reconstruction method / computed tomography / hard x-ray imaging / singular value decomposition / QR decomposition / fast algorithm / minimum GCV criterion |
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| Research Abstract |
Linear algebraic methods of image reconstruction from integral transform values have been developed for the purpose of plasma diagnostics, and examined in applications to the computed tomography (CT) of laboratory plasmas and to a hard X-ray imaging of the sun.
1.(1) The Tikhonov-Phillips regularization method, that is, the standard method using the singular value decomposition for solving ill-posed linear equations, and (2) a new method based on a triple use of the QR decomposition (QRD) were examined and compared in application to a visible line emission CT in a small tokamak of Nagoya University. Fourier-like analysis was made in regarding the numerically generated basis systems of image and projection, and the two methods were found practically equivalent in imaging.
2.Improving the QRD method was made on a more efficient algorithm of double QRD and on using the generalized cross validation (GCV) as a statistical criterion for optimization. Good results with a notable reduction in computing time was obtained on the above CT experiment.
3.The above methods were applied to the data processing of the hard x-ray telescope (HXT) onboard the solar observation satellite Yohkoh, and poor results were obtained in imaging the narrow peaks of solar flare. Useful aspect was obtained on the excellence of the maximum entropy method, that is, a nonlinear regularization which gave a superresolution in imaging from very small number of data.
4.The Tikhonov regularization and its optimization with GCV were applied on the ill-posed normal equation in series expansion method and examined on the soft x-ray emission CT in the French tokamak Tore Supra with strong angular limitation and low SN ratio. Imrovement was obtained on the Fourier-Bessel expansion model having higher modes for MHD oscillation imaging.
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