基于六边对称变换群的快速CT重建算法  

Fast computed tomography reconstruction algorithm based on a hexagonal symmetric transformation group

作　　者：王一多[1,2] 席平[1] 薛威[1,3] 

机构地区：[1]北京航空航天大学机械与自动化学院,北京100191 [2]北京化工大学理学院,北京100029 [3]北京化工大学北方学院,河北燕郊065201

出　　处：《北京化工大学学报（自然科学版）》2010年第4期135-140,共6页Journal of Beijing University of Chemical Technology(Natural Science Edition)

基　　金：国家"863"计划(2007AA04Z125)

摘　　要：利用正六边形在所有能铺满整个平面的正多边形中具有最多对称轴的特点(共6条,正三角形3条,正方形4条),结合对称变换群的性质对计算机断层扫描重建(CT)中的滤波反投影算法(FBP)进行了优化,降低了算法中反投影部分的计算复杂度,从而得到一个快速重建算法。由于反投影的计算在FBP算法中耗时最多,所以新算法明显加快了图像重建速度,通过仿真试验与已有快速重建算法进行比较,表明文中算法在同等条件下重建速度提高明显。After optimizing the filter back projection （FBP） algorithm of computed tomography （CT） using the theory of symmetric transformation groups and the fact that a regular hexagon has the most symmetry axes among all the regular polygons which can pave a two dimensional plane without gaps （a total of 6 symmetry axes compared with 3 for a regular triangle and 4 for a square）,a fast reconstruction algorithm has been constructed to reduce calculation time costs in the back projection part of FBP. Since the back projection part is the major time-consuming part of FBP,the new algorithm accelerates image reconstruction significantly. Compared with some other accelerating algorithms described recently,the reconstruction speed of the proposed method is superior.

关 键 词：计算机断层扫描 正六边形 对称变换群 滤波反投影 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]