正子斷層掃描中可平行化之混合型加速的ECM和SAGE演算法

Abstract

正子斷層掃描 (PET) 是用來診察出人體內部新陳代謝活動的醫學設備,利 用最大概似估計法重建新陳代謝的強度是相當普遍的方法.EM或ECM演算法 利用列運算的疊代方式來尋找最大概似估計量. 這些演算法具有單調收 斂,線性複雜度,和保持非負解的特性. 同時,它們亦可平行化. 然而,它們 的收斂速率相當慢. 文獻上有許多不同的加速方法. 其中,SAGE或AECM演 算法改變完整資料空間 (complete data space) 的選擇來有效地加速收 斂速率. 它們亦具有單調收斂,非負解及線性複雜度的特性. 然而,這些演 算法無法平行化. 我們建議運用混合型加速的HSAGE及HECM演算法來進一 步加快收斂速率. 新演算法保持單調收斂,線性複雜度及非負解的特性,同 時, 新演算可以適用於平行處理. 這些特性使得新演算法是實際且可行 的. Positron emission tomography (PET) is a medical diagnosis equipment used to study metabolisms inside a human body. The maximum likelihood estimates (MLE) that is aimed to reconstruct the intensity of positron emission has become very popular among researchers in PET. The expectationmaximization (EM) or expectation/conditional maximization (ECM) algorithms are a row operation iterative approach to find the maximum likelihood estimate with monotonic convergence, linear complexity and nonnegativeness preserving. They are also parallelizable. However, the convergence rates are slow. A variety of accelerated methods had been proposed in literature. Among them, the space-alternating generalized expectation maximization (SAGE) or the alternating expectation/conditional maximization (AECM) algorithm accelerates the convergence rate effectively by alternating the complete data space. It is monotonic convergent, nonnegativeness preserving and of linear complexity.However, they are not parallelizable. We proposed a hybrid SAGE (HSAGE) anda hybrid ECM (HECM) algorithms to further speed up the convergence rates.The new algorithms retain monotonic convergence, linear complexity and nonnegativeness preserving. Furthermore, the new algorithms are easily parallelizable, which make them more practically appealing.