中文摘要：

正电子发射型计算机断层成像（PET）作为一种重要的临床影像技术，其图像重建技术非常重要。本文将γ光子飞行时间信息（TOF）加入到系统响应矩阵并提出基于 TOF 的图像重建算法。基于压缩感知原理，利用全变差和小波变换对图像进行稀疏化，以它们为正则项构建目标函数；并运用惩罚函数的方法将目标函数求解分解为二次优化和稀疏约束2个子问题，运用交替求解的方法逐一求解，降低了求解的复杂性。采用蒙特卡罗对Derenzo模型进行仿真重建并比较不同算法的成像效果，结果表明，加入 TOF 信息和利用稀疏约束能够更好地拟制噪声，图像重建效果优于传统算法。文中进一步研究了系统时间分辨率和时间采样间隔对图像重建的影响，结果表明，时间分辨率越高、时间采集间隔越短，重建效果越好。

英文摘要：

Positron emission tomography （PET） is an important clinical imaging technology, the image recon-struction of it is important. In this paper the time of flight （TOF） information ofγ photon was added to the system response matrix. According to the compressed sensing theory, the signal was sparsified with the total variation and wavelets transform, and they were used as regularization to construct the objective function. Using the pen-alty function method, the objective function was decomposed into two sub-problems of solving quadratic optimization and sparse regularization with the idea of penalty function, and the alternative iteration methods were used to reduce the solution complexity. The Monte Carlo simulations with Derenzo phantom were applied to compare the efficiency of different algorithms, and the results show that the proposed methods perform better than the traditional algorithms. The thesis further investigated the effect of the system temporal resolution and time acquisition interval on the quality of the image reconstruction, the results show that the higher time resolution and shorter acquisition time interval can get better reconstruction results.