【作者】 邱钧； 徐茂林； 张兆田； 范惠荣；

【Author】 QIU Jun XU Mao-lin ZHANG Zao-tian FAN Hui-rong

【机构】 北京信息工程学院应用数学研究室； 国家自然科学基金委员会信息科学部；

【摘要】 用级数展开法由投影重建图象计算量大、重建速度慢,其中投影矩阵系数的计算是重要因素之一。本文指出投影数据存在几何对称结构,从而简化了相应投影矩阵系数的算法;由此给出了图象重建的对称块快速迭代算法。并对模拟和实测数据进行了图像重建实验。结果表明:与常规算法比较,对称块迭代算法不仅重建速度快,而且重建图象精度高。级数展开法重建图象的经典方法是R.Gorden 等提出的ART 法,及P.Gilbert 首创的SIRT法。其后发展的多种算法大致可从两个方面分类。一是以优化理论为基础的各种迭代算法。二是对两种经典迭代格式的修正,如Eggerment 等将ART 中的Kacmarz 迭代改进为固定块迭代,Censor 及Herman 进一步改进为可变块迭代,使经典迭代法形成一个统一的框架。更多还原

【Abstract】 With a method of series expansion for image reconstruction,there exists great difficulties interms of slow reconstruction due to bulk data to deal with.It is evident that one of the key factors is howto work out the accurate coefficients of projection matrix.This paper presents the geometrical symmetryprinciple of projection data for image reconstruction and provides a simplified algorithm for thecoefficients of projection matrix via this symmetrical principle,thereby an ad hoc method of fastsymmetric block-iterative is introduced to solve the image reconstruction problem.The experimentalimage reconstruction utilizing the symmetric algorithm with both simulated and experimental projectiondata is undertaken.In comparison with the performance of other conventional algorithms,the resultsshow that the image reconstruction using the presented algorithm is much faster,and the reconstructionimages has much better precision than the others.更多还原