文档介绍：基于Monte Carlo模拟的系统矩阵解析算法*
凌松云,曹文田,李军,蔡白银,包尚联
(北京大学医学物理和工程北京市重点实验室北京 100871)
摘要:系统矩阵是单光子发射计算机断层成像系统(SPECT)中迭代重建算法的关键因素。蒙特卡洛(MC)模拟是计算系统矩阵最准确、最常用的方法,但是标准的MC算法最大的缺点就是耗时太长。为此,提出一种新的解析算法:利用MC模拟的投影数据,拟合准直器的点扩散函数,并以此作为计算系统矩阵的解析表达式。该新算法既缩短了计算耗时又包含了MC投影信息,使得解析计算的系统矩阵与MC模拟的结果相当。因此,该方法可用于修正准直器张角效应对系统矩阵计算的影响。本文采用解析计算得到的系统矩阵,重建了均匀泛源和Jaszczak模型的MC投影图像,重建图像能真实的反映原始图像。
关键词:蒙特卡洛;系统矩阵;准直器张角效应;点扩散函数
中图分类号:Q334 文献标识码:A 国家标准学科分类代码:
Analytical algorithm for system matrix based on Monte Carlo simulation
Ling Songyun, Cao Wentian, Li Jun, Cai Baiyin, Bao Shanglian
(Beijing Key Laboratory of Medical Physics & Engineering, Peking University, Beijing 100871, China)
Abstract:System matrix is the key element in the iterative reconstruction algorithm for SPECT (single photon puted tomography). Monte Carlo (MC) simulation is the most accurate mon method to calculate system matrix. However, the major disadvantage of the standard MC algorithm is the puting time it may take. Therefore, a new method is proposed here, which adopts the projection data attained from MC simulation to fit a point spread function (PSF) of the collimator. Then this function is taken as the analytical expression to calculate the system matrix. This new method not only shortens puting time, but also contains the MC information, which makes the system matrix calculated using this analytical parable with the result of MC simu