Abstract: Positron emission tomography(PET) is an important clinical imaging technology, the image reconstruction of it is important. In this paper the time of flight(TOF) information of γ 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 penalty 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.