Recently, the limited-angle TOF-PET system has become an active research topic due to the considerable reduction of hardware cost and potential applicability for performing needle biopsy on patients while in the scanner. This undersampling measurement configuration oftentimes suffers from the deteriorated reconstructed images. However, the established theory of Compressed Sampling (CS) provides a potential framework for undertaking this problem, given that the imaged object can be sparse in some transformed domain. In here, we studied using numerical simulations the application of sparsity-promoted framework to TOF-PET imaging for two undersampling configurations. From these simulations, a relationship was obtained between the number of detectors (or the range of angle) and TOF time resolution, which provided an empirical guide of designing a low-cost TOF-PET systems while ensuring good reconstruction quality. Another contribution is the exploration of p-TV regularization, which showed that RMSE (Root of Mean Square Error) and SSIM (Structural Similarity) were optimized when p = 0.5. Several sets of representative numerical experiments were executed to validate the proposed methodology, which demonstrates the promising applicability of undersampling TOF-PET imaging.