代数的画像再構成法における部分空間の直交性を利用した新しい並列計算法

概要

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The algebraic reconstruction technique (ART) solves image reconstruction problems, regarding them as simultanous linear equations. This algorithm applies the sequential projection onto a hyperplane constructed by each equation. The ART is able to reconstruct images even if sufficient projection data is not obtainable. On the other hand, parallel computing algorithms suitable for the recently increasing multiprocessor systems are required. A parallel algorithm using simultaneous projection has been proposed by Censor et al. (2001). However, the original ART algorithm is not suitable for parallel computing because it uses sequential projection. In this study, we propose a new parallel iterative method using the ART algorithm. In this method, we divide the simultaneous linear equations into blocks that contain the equations obtained from one projection. Then we apply the ART algorithm to each block, and calculate the average of the solutions from them. This average is the solution of a simultaneous equation system, (i. e., a reconstructed image. Evaluating the result of reconstruction simulations with our method, in terms of convergence speed and the quality of reconstructed images, verifies the high efficiency of the new method.
2003-12-10