疊代式正子影像重建之幾何因素研究

正子斷層造影技術能藉由正子互毀反應產生同符事件，提供活體功能性的生理資訊和影像。疊代式影像重建演算法的優點，在於能利用帕松分佈模型描述光子行?，並同時考慮幾何與其他物理因素，以減少假影的產生。然而過去有關幾何模型對於影像重建的影響，並無多所著墨。所以本實驗想要探討不同的幾何模型，以最大相似度與均值最大化演算法?架構，驗證幾何模型對疊代影像重建法之收斂速度的影響。實驗中將研究內插法模型(interpolative model)、面積法模型(area-based model)、立體角模型(solid-angle model)，就點射源的重建過程，搭配帕松分佈取樣與均勻背景活度的改變，觀察各幾何模型對影像重建速度的影響。也針對點射源的模擬重建結果與蒙地卡羅方法的結果比較，驗證其一致性。在有統計雜訊和背景活度的情況下，由相似度函數曲線的結果發現，立體角模型相較於其他兩種幾何模型，能有較高的相似度函數值，代表其收斂速度較快。因此幾何模型的改變，是會影響影像重建的收斂過程。而以使用較能描述真實現象的立體角幾何模型進行重建，在因定疊代次數的條件下，則會有較佳的收斂速度與相似度較高的重建影像。
Positron emission tomography (PET) is a powerful imaging tool which can provide physiological information using molecular tracers. The main advantages of iterative reconstruction algorithm are that it allows Poisson modeling to describe coincident photon pairs, and permits the inclusion of many physical factors to reduce unfavorable artifacts. The thesis of this work is to investigate various geometric models and their influence on algorithm convergence of iterative image reconstruction. We consider three geometric models: interpolative, area-based and solid-angle. The iterative algorithm to evaluate the convergence performance is the Maximum Likelihood Expectation and Maximization (MLEM) algorithm. From the plot of log-likelihood curves, the sold-angle model can reach the highest value at early iterations. It means that the MLEM algorithm with solid-angle model will converge faster than the other models. In addition, the image results generated by solid-angle model exhibit better contrast recovery. Therefore, the solid-angle model is a favorable geometric model for iterative PET image reconstruction.