Erdogan H, Fessler J A
University of Michigan, Ann Arbor 48109-2122, USA.
Phys Med Biol. 1999 Nov;44(11):2835-51. doi: 10.1088/0031-9155/44/11/311.
The ordered subsets EM (OSEM) algorithm has enjoyed considerable interest for emission image reconstruction due to its acceleration of the original EM algorithm and ease of programming. The transmission EM reconstruction algorithm converges very slowly and is not used in practice. In this paper, we introduce a simultaneous update algorithm called separable paraboloidal surrogates (SPS) that converges much faster than the transmission EM algorithm. Furthermore, unlike the 'convex algorithm' for transmission tomography, the proposed algorithm is monotonic even with nonzero background counts. We demonstrate that the ordered subsets principle can also be applied to the new SPS algorithm for transmission tomography to accelerate 'convergence', albeit with similar sacrifice of global convergence properties as for OSEM. We implemented and evaluated this ordered subsets transmission (OSTR) algorithm. The results indicate that the OSTR algorithm speeds up the increase in the objective function by roughly the number of subsets in the early iterates when compared to the ordinary SPS algorithm. We compute mean square errors and segmentation errors for different methods and show that OSTR is superior to OSEM applied to the logarithm of the transmission data. However, penalized-likelihood reconstructions yield the best quality images among all other methods tested.
有序子集期望最大化（OSEM）算法因其对原始期望最大化（EM）算法的加速作用以及易于编程，在发射图像重建中备受关注。透射EM重建算法收敛非常缓慢，在实际中并不使用。在本文中，我们介绍了一种名为可分离抛物面替代（SPS）的同步更新算法，其收敛速度比透射EM算法快得多。此外，与用于透射断层扫描的“凸算法”不同，即使在存在非零背景计数的情况下，所提出的算法也是单调的。我们证明，有序子集原理也可应用于用于透射断层扫描的新SPS算法，以加速“收敛”，尽管与OSEM一样会牺牲一些全局收敛特性。我们实现并评估了这种有序子集透射（OSTR）算法。结果表明，与普通SPS算法相比，OSTR算法在早期迭代中能使目标函数的增加速度加快大致与子集数量相同的程度。我们计算了不同方法的均方误差和分割误差，并表明OSTR优于应用于透射数据对数的OSEM。然而，在所有测试的其他方法中，惩罚似然重建产生的图像质量最佳。
