2回QR分解と最小GCV規準による疎データCT像再構成

概要

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The linear algebraic technique of image reconstruction is developed by using the QR decomposition (QRD) instead of the singular value decomposition (SVD). A new algorithm of double QRD, which is superior to SVD greatly in computational complexity, is proposed for generating a couple of orthonormal basis systems. Also, the generalized cross validation (GCV) for the SVD-based method of Tikhonov-Phillips (TP) is extended in order to optimize the regularization parameter. In application to sparse-data computed tomography of plasma with pixels and detectors as many as hundreds, the new method has proved successful for synthesizing good images, which are very similar to those of the TP method, with a satisfactory behavior of GCV. This well-implemented method of image reconstruction is described and, then, the results of numerical simulation and experimental data analysis are exhibited in this paper.
大同工業大学の論文