正子斷層掃瞄的混合型簡易演算法

Abstract

由於EM和GEM演算法的收斂速度慢，在文獻上已有數種加速收斂的方法被提出。例如SAGE演算法 (Fessler 和 Hero 1994)，ACEM演算法 (Meng和Van Dyk1997) 、、、等方法，運用假設的完全資料空間 (complete data space) 的改變，以加速GEM演算法的收斂速度，並保持GEM演算法的原有特性。另一方面，Thiesson，Meek，和Heckerman (1999) 提出簡易的ＥＭ演算法 (Lazy EM algorithm，簡記為LEM演算法) 以處理大量的資料。 我們計劃運用LEM演算法的概念，重建正子斷層掃瞄影像。文獻上原來的LEM演算法並不適用於正子斷層造影，本篇論文因而發展出新的方法重建正子斷層掃瞄影像。可是這種LEM演算法未具單調收斂性；為了使其具有單調收斂性，我們提出混合型的加速方法和LEM演算法結合。我們更進一步結合完整資料空間(complete data space)的改變，以維持單調收斂性，加快收斂速度，同時保持GEM演算法的原有優點。上列的方法將利用臺北榮民總醫院收集到的實證資料來驗證上列所提的方法，並進行比較研究。

Because of slow convergence of EM algorithm, another variants of generalized EM (GEM) algorithms, such as the SAGE (Fessler and Hero, 1994), ACEM (Meng and van Dyk, 1997) algorithm, and so forth, were proposed in literature. They were applied to accelerate the convergence speed of the GEM algorithm by the augmentation of complete data space and preserve the merits of GEM algorithms. On the other hand, in order to reduce the computation complexity, unit computation cost per iteration and memory requirement, Thiesson, Meek, and Heckerman (1999) suggested an modification, called the lazy EM (LEM) algorithm, to handle large mount of data. Motivated by the above development, we investigate the possibility of applying the idea of LEM algorithm for PET image reconstruction. The original LEM algorithm in the literature is not feasible for PET and a new way of LEM algorithm is proposed in this thesis. However, the algorithm fails to converge monotonically. To preserve the monotonic convergence and accelerate its convergence speed, we combine the new method with hybrid accelerators. Furthermore, combining with the augmentation of complete data space, these new methods can accelerate convergence speeds as well as maintain the merits of GEM algorithms. The methods are tested by the empirical data collected at the Veterans General Hospital (V.G.H.)-Taipei PET system.