Hsiao Ing-Tsung, Rangarajan Anand, Khurd Parmeshwar, Gindi Gene
School of Medical Technology, Chang Gung University, Kwei-Shan, Tao-Yuan 333, Taiwan.
Phys Med Biol. 2004 Jun 7;49(11):2145-56. doi: 10.1088/0031-9155/49/11/002.
We propose an algorithm, E-COSEM (enhanced complete-data ordered subsets expectation-maximization), for fast maximum likelihood (ML) reconstruction in emission tomography. E-COSEM is founded on an incremental EM approach. Unlike the familiar OSEM (ordered subsets EM) algorithm which is not convergent, we show that E-COSEM converges to the ML solution. Alternatives to the OSEM include RAMLA, and for the related maximum a posteriori (MAP) problem, the BSREM and OS-SPS algorithms. These are fast and convergent, but require ajudicious choice of a user-specified relaxation schedule. E-COSEM itself uses a sequence of iteration-dependent parameters (very roughly akin to relaxation parameters) to control a tradeoff between a greedy, fast but non-convergent update and a slower but convergent update. These parameters are computed automatically at each iteration and require no user specification. For the ML case, our simulations show that E-COSEM is nearly as fast as RAMLA.
我们提出了一种名为E-COSEM(增强型完全数据有序子集期望最大化)的算法,用于发射断层扫描中的快速最大似然(ML)重建。E-COSEM基于增量期望最大化方法。与不收敛的常见有序子集期望最大化(OSEM)算法不同,我们证明E-COSEM收敛于最大似然解。OSEM的替代算法包括RAMLA,对于相关的最大后验(MAP)问题,有BSREM和OS-SPS算法。这些算法快速且收敛,但需要明智地选择用户指定的松弛策略。E-COSEM本身使用一系列依赖于迭代的参数(大致类似于松弛参数)来控制在贪婪、快速但不收敛的更新与较慢但收敛的更新之间的权衡。这些参数在每次迭代时自动计算,无需用户指定。对于最大似然情况,我们的模拟表明E-COSEM几乎与RAMLA一样快。