A row-action alternative to the EM algorithm for maximizing likelihoods in emission tomography
A row-action alternative to the EM algorithm for maximizing likelihoods in emission tomography
复制标题
DOI：
10.1109/42.538946
复制
发表时间：
1996-10-01
影响因子：
10.6
通讯作者：
DePierro, AR
中科院分区：
文献类型：
--
作者：
Browne, J;DePierro, AR
用最大似然（ML）方法来估计人体截面上的放射性分布已经在发射计算机断层扫描（ECT）研究人员中非常流行，因为与传统的滤波反向投影（FBP）算法产生的图像相比，它已经被证明提供了非常好的图像。期望最大化（EM）算法是ECT中常用的泊松似然最大化的迭代方法，因为它具有诱人的理论和实用特性。它的主要缺点是，由于收敛速度慢，通常需要大量的计算才能获得可接受的图像。在本文中，我们提出了一种行作用最大似然算法（RAMLA）作为EM算法的替代方案，用于最大化ECT中的泊松似然。我们推导了该算法的收敛特性，并通过计算机模拟的方式证明，RAMLA的早期迭代比标准EM算法更快地提高了ECT中的泊松似然。具体来说，我们表明，从测量模拟脑幻影中总放射性核素摄取的角度来看，RAMLA的迭代1、2、3和4的表现至少与EM的迭代45、60、70和80一样好。此外，我们表明RAMLA的迭代1、2、3和4分别获得了与迭代45、60、70和80相当的可能性值。本文还提出了一种改进的快速有序子集EM （OS-EM）算法，并证明RAMLA算法是这种改进的OS-EM算法的一个特例。此外，我们证明了我们的修改收敛于ML解决方案，而标准OS-EM则没有。
The maximum likelihood (ML) approach to estimating the radioactive distribution in the body cross section has become very popular among researchers in emission computed tomography (ECT) since it has been shown to provide very good images compared to those produced with the conventional filtered backprojection (FBP) algorithm. The expectation maximization (EM) algorithm is an often-used iterative approach for maximizing the Poisson likelihood in ECT because of its attractive theoretical and practical properties. Its major disadvantage is that, due to its slow rate of convergence, a large amount of computation is often required to achieve an acceptable image. In this paper we present a row-action maximum likelihood algorithm (RAMLA) as an alternative to the EM algorithm for maximizing the Poisson likelihood in ECT. We deduce the convergence properties of this algorithm and demonstrate by way of computer simulations that the early iterates of RAMLA increase the Poisson likelihood in ECT at an order of magnitude faster that the standard EM algorithm. Specifically, we show that, from the point of view of measuring total radionuclide uptake in simulated brain phantoms, iterations 1, 2, 3, and 4 of RAMLA perform at least as well as iterations 45, 60, 70, and 80, respectively, of EM. Moreover, we show that iterations 1, 2, 3, and 4 of RAMLA achieve comparable likelihood values as iterations 45, 60, 70, and 80, respectively, of EM. We also present a modified version of a recent fast ordered subsets EM (OS-EM) algorithm and show that RAMLA is a special case of this modified OS-EM. Furthermore, we show that our modification converges to a ML solution whereas the standard OS-EM does not.