貝氏定理影像重建演算法是1990年Green將最大相似度評估法和最大事後機率評估法結合所產生的一步延遲期望值最大演算法(One-Step-Late Expectation Maximum, OSL)，使用在正子斷層掃描上進行影像重建時可以搭配不同的影像事前機率(Image prior)來做不同方式的雜訊抑制，但在這個過程中影像事前機率的影響有可能會使重建影像過度平滑(over-smoothing)或是在邊緣部分產生其他問題。飛行時間正子斷層掃描(Time-of-Flight PET)能提供互毀光子被偵檢器接收到的時間差，增加重建影像的解析度，提升影像訊雜比。在本研究中提出將貝氏定理影像重建演算法用於重建TOF PET影像，包含TOF-OSL與TOF-OSEM-OSL重建法，並和傳統PET使用OSL與OSEM-OSL重建法所重建的影像做比較，利用TOF技術改善貝氏定理影像重建法的缺點，在保留影像事前機率的貢獻下，增加了TOF的時間資訊優勢，進而提升影像品質。

A Bayesian image reconstruction algorithm, One-Step-Late (OSL) algorithm which combines maximum likelihood expectation maximization (MLEM) with maximum a posteriori (MAP) estimation, was derived by Green in 1990. In Positron emission tomography (PET), image reconstruction using OSL combines the likelihood function with image prior. Use different way to reduce the effect of noise in the data with different image prior. However, image prior may over-smooth small objects and edges. Time-of-Flight PET system can provide time difference of annihilation photon pair and this TOF characteristic can improve image resolution and signal-to-noise ratio (SNR). In this study, we proposed a TOF iterative image reconstruction algorithm based on the Bayesian scheme. Using TOF technique can improve the image quality of image which reconstructed by Bayesian image reconstruction algorithm. The results of TOF-OSL and TOF-OSEM-OSL would be compared with the results of OSL and OSEM-OSL. TOF Bayesian image reconstruction algorithm can provide not only noise reduction but also can improve the image quality in PET.

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