标题: 正子断层扫描影像的实证研究及混合型加速的GEM演算法
Emperical Studies and Hybrid Accelerators of Genneralized EM Algorithms for PET
作者: 陈泰宾
Tai-Been Chen
卢鸿兴
Henry Horng-Shing Lu
统计学研究所
关键字: 正子断层扫描影像;单调收敛性;SAGE;hybrid AECM;positron emission tomography;EM algorithm;SAGE;hybrid AECM
公开日期: 1998
摘要: 中文摘要
由于资料的不完整及随机性质,对于正子断层扫描影像(PET)的重建是一件很困难的工作。利用EM 演算法求得最大概似估计量(MLE) 以重建正子断层扫描影像强度是文献上建议的方法。此种方法具有列运算、线性复杂度、单调收敛性、非负解以及可平行化的特性。针对台北荣民总医院的PET系统,我们进行实证研究,比较由MLE-EM演算法及仍在商业系统上运用的FBP (Filtered Backprojection) 演算法所重建的影像,并进一步设计实验来估计随机偶合事件 (Random Coincidence Events)。
但是EM演算法的收敛速度慢,故文献上己有数种不同的加速方法。例如:SAGE、AECM等方法,进一步改变完整资料空间的选择,以加快收敛速度,同时保持一些EM演算法的优点。可是这些方法郤无法平行化,因此我们提出混合型加速的GEM演算法,同时保持EM演算法的特性,更可以加快收敛速度及进行平行化。本篇论文研究HSAGE、HEM (Hybrid SAGE、 Hybrid EM) 演算法,并应用在实证的资料上。
Abstract:
The reconstruction of a medical image in positron emission tomography (PET) is difficult due to the indirect and random observations in a large system. The maximum likelihood estimate with the EM algorithm (MLE-EM) was proposed in literature to reconstruct the intensity of positron emission of PET with the merits of row operation, linear complexity, monotonic convergence, nonnegativeness, and parallelizability. Based on the empirical studies of the Veterans General Hospital (V.G.H.)-Taipei PET system, we will compare the reconstruction results of the MLE-EM with those of filtered backprojection (FBP) that are routinely used in commercial systems. Furthermore, experiments are designed to explore the random coincidence events by the MLE-EM.
One of the disadvantages about EM algorithm is its slow convergence speed. Various accelerated methods had been proposed in literature, like the space-alternating generalized expectation maximization (SAGE) or the alternative expectation/conditional maximization (AECM) algorithms. They preserve the merits of row operation, linear complexity, monotonic convergence, and nonnegativeness. But they are not parallelizable. Combined with the search along the generalized gradient direction that increases the incomplete space log-likelihood, hybrid accelerators can further improve the convergence speeds of these generalized EM algorithms. Meanwhile, all the merits of the generalized EM algorithms are preserved. The resulting new algorithms, include the hybrid EM and hybrid SAGE (or hybrid AECM) algorithms, are studied based on the empirical data in this thesis.
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT870337007
http://hdl.handle.net/11536/63996
显示于类别:Thesis