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

从积分变换值重建图像的线性代数方法已经发展到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验。(1)在名古屋大学小型托卡马克可见光线发射CT的应用中，研究并比较了Tikhonov-Phillips正则化方法（即利用奇异值分解求解病态线性方程的标准方法）和基于QR分解（QRD）三重使用的新方法。对数值生成的图像基系统和投影基系统进行了类傅里叶分析，发现这两种方法在成像上是等效的。对QRD方法进行了改进，提出了一种更有效的双QRD算法，并将广义交叉验证（GCV）作为优化的统计准则。在上述CT实验中获得了较好的结果，计算时间明显缩短。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，对太阳耀斑窄峰的成像效果较差。利用最大熵法的优点，即非线性正则化，获得了小数据量成像的超分辨率。将Tikhonov正则化及其GCV优化应用于级数展开法中的病态正态方程，并在角度限制强、SN比低的法国托卡马克Tore Supra软x射线发射CT上进行了验证。对具有较高模态的傅里叶-贝塞尔展开模型进行了改进。

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.