飛行時間正子斷層掃描系統(Time-of-flight positron emission tomography, TOF PET)除了能提供傳統PET高空間解析度的功能性影像外，更具有高時間解析度的優勢，使得偵收系統能夠測量互毀光子對到達偵檢器的時間差，進而改善影像品質。然而，在TOF PET成像時，因偵收資料包含空間資訊和時間資訊，因此TOF PET影像重建耗費的時間較傳統PET影像重建多。本研究建立一個飛行時間資料的統計模型，針對TOF PET重建過慢的問題，應用PET快速疊代演算法並加入TOF PET的時間資訊，以加速影像重建的速度。模擬實驗結果顯示，相較於傳統PET重建影像，TOF PET重建影像有較高的訊雜比和較高的對比恢復性。另外在快速疊代演算法的部分，相較於傳統的TOF PET加速演算法，本研究提出的飛行時間加速演算法能進一步提升收斂速度。整體而言，在不影響TOF PET高品質的前提下，本研究所提出的TOF PET加速演算法能確實達到加速影像收斂的目的。

The time-of-flight (TOF) positron emission tomography(PET) system can provide not only high spatial resolution in functional image as conventional PET but high time resolution. High time resolution provides the measurement ability of time difference of annihilation photon pair reach detector. The characteristic can improve image quality. In TOF PET imaging, the measurement data contain spatial and temporal information. TOF PET image reconstruction takes consequently more time than conventional PET. In this study, we contributed a two-dimension statistical model for TOF data. We also developed a fast TOF iterative image reconstruction algorithm to improve low convergence rate of TOF image reconstruction. The results of experiments show that TOF reconstruction can obtain higher signal-to-noise ratio (SNR) and higher contrast recovery rate than conventional PET. The fast TOF iterative image reconstruction we derived have faster convergent rate than conventional one. In conclusion, the TOF PET fast iterative method we derived can achieve the acceleration of image reconstruction without spoiling high image quality characteristics of TOF PET.

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