正子斷層造影(Positron Emission Tomography，PET)技術能藉由正子互毀反應產生同符事件，提供功能性的生理資訊。統計式疊代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為，和考慮幾何因素以減少假影的產生。然而在過去，幾何模型對於影像重建的影響，並沒有被仔細地討論。所以本實驗想要藉由討論不同的幾何模型，與最大相似度與均值最大化演算法之間的關係，驗證幾何模型是否會影響重建法。實驗中將以內插法模型(Interpolative Model)、面積法模型(Area-based Model)、立體角模型(Solid Angle Model)，進行點射源的重建過程。由相似度函數曲線的結果，發現面積法模型與立體角模型有較快的收斂速度。在有統計雜訊、有背景活度的情況下，跟其他兩幾何模型比較起來，立體角模型的相似度函數值較高。因此，我們初步認為幾何模型的改變，會影響影像重建的過程。而以較能描述真實現象的幾何模型進行重建，如立體角模型，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 statistical iterative reconstruction algorithm can apply Poisson modeling to describe coincident photon pairs, and permit 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 statistical 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.

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