Linear algebraic methods of image reconstruction and their applications to plasma measurements.

图像重建的线性代数方法及其在等离子体测量中的应用。

• 批准号: 08680511
• 负责人: IWAMA Naofumi
• 金额: $ 1.54万
• 依托单位: Toyama Kenritu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08680511/
• 关键词: plasma measurement; image reconstruction method; computed tomography; hard x-ray imaging; singular value decomposition; QR decomposition; fast algorithm; minimum GCV criterion; プラズマ撮像; 像画構成法

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.

从积分变换值的图像重建的线性代数方法已开发用于等离子体诊断的目的，并在实验室等离子体的计算机断层扫描（CT）和太阳的硬X射线成像的应用中进行了检查。(1)在名古屋大学小型托卡马克装置的可见线发射CT中，对Tikhonov-Phillips正则化方法，即用奇异值分解求解病态线性方程组的标准方法和（2）基于QR分解（QRD）的三重使用的新方法进行了检验和比较。对数值生成的图像基系统和投影基系统进行了类傅立叶分析，发现两种方法在实际成像中是等价的。2.对QRD方法进行了改进，提出了一种更有效的双QRD算法，并采用广义交叉验证（GCV）作为优化的统计准则。将上述方法应用于太阳观测卫星Yohkoh上的硬X射线望远镜（HXT）的数据处理中，对耀斑窄峰的成像效果不佳。利用最大熵方法的优点，即非线性正则化方法，可以在极少量数据的情况下实现超分辨率成像。4.将Tikhonov正则化方法及其GCV优化方法应用于级数展开法中不适定的正则方程，并在法国Tore Supra托卡马克装置的软X射线发射CT上进行了强角度限制和低信噪比条件下的验证。改进了具有高次模的傅里叶-贝塞尔展开模型，使之适用于磁流体振荡成像。

项目成果

N.Terasaki, N.Iwama and Y.Hosoda: "Sparse-data CT image reconstruction by the method of Tikhonov-Phillipsregularization and GCV : its application to plasma Images." Trans.of IEICE D-II. vol.J81-D-II,no.1. 93-100 (1998)

N.Terasaki、N.Iwama 和 Y.Hosoda：“通过 Tikhonov-Phillips 正则化和 GCV 方法进行稀疏数据 CT 图像重建：其在等离子体图像中的应用。”