基於現代的單光子放射電腦斷層掃描系統求精於成像程序的速度和解析度的提升，本論文將圖形處理器(Graphics Processing Unit, GPU)應用於伽瑪射線位置估算和斷層掃描影像重建演算法。 位置估算演算法由最大可能性值估算法(Maximum-Likelihood Estimator)配合多變數常態分佈模型(Multivariate Normal Model)建立，並且利用截尾重心法配合收縮格點尋找法(Truncated Center of Gravity + Contracting Grid Search)，快速而準確的估算每一筆伽瑪射線事件的發生位置，一秒可估算400,000筆事件，且保有良好的準確率。利用位置估算法及規則格點圖像(Regular Grid Pattern)檢視所開發之伽瑪相機解析度，初步得知相機解析度至少可優於2 mm。 斷層掃描影像重建使用序列子集之期望值最大化演算法(Order Subset Expectation Maximization, OSEM)，且將動態運算(On The Fly Computation)應用在緻密立體像素格點之影像系統矩陣作正向投影與反向投影，快速地重建出高解析度之三維立體影像;使用數百萬個立體像素之影像系統矩陣進行三維影像重建僅需要數分鐘，達到高效率的成像程序。 ;The aim of this study is to achieve fast image processing for a micro-SPECT system. Iterative algorithms are developed with powerful graphics processing units (GPUs) to perform position estimations and tomographic reconstructions. The position estimator is constructed with the maximum-likelihood principle and the multivariate normal model. By using the truncated center of gravity combined with contracting grid search (TCOG-CGS), the algorithm can estimate the positions of gamma ray events rapidly and accurately. The processing speed is about 400,000 events per second for a gamma camera of 49 × 49 pixels with 1 mm pixel width. Also, the camera resolution is visualized by a regular grid pattern and the 2 mm grid spacing is resolvable. For tomographic reconstructions, the ordered-subset expectation maximization (OSEM) algorithm is implemented with an imaging system matrix containing millions of voxels. To solve the memory storage issues, we bring in the concept of on-the-fly computation to the forward projection and backward projection of imaging system matrix. The GPU-based algorithm can reconstruct the 3D image with several millions of voxels in a few minutes, and is 19 times faster than the CPU-based algorithm.
