A novel TOF PET reconstruction method from limited-view data based on TV-minimization

PET detectors provide the information of the position, the energy and the timing about the decay events on the LOR. Traditional PET image reconstruction has not taken the timing information into account, only used the timing information for coincidence judgments. The high timing resolution PET detectors provide very precise TOF information, then TOF image reconstruction method which utilizes the timing information of PET detectors is so crucial for the TOF PET system. We take advantage of timing information provided by a pair of TOF PET detectors, and then reconstruct the activity distribution from the limited-view projection data. Since the image reconstruction from the limited-view data is an under-determined problem mathematically, conventional algorithms cannot achieve the exact reconstruction of the limited-view problem. In this work, we propose a half-analytic and half-iterative method named DF/LBM (Direct Fourier and Logarithmic Barrier Method) to solve the limited-view problem with the TOF information. The least square solution is obtained via DFM (Direct Fourier Method), and then a convex optimization method named logarithmic barrier method is employed to correct the least square solution. The substance of the convex optimization is defining the components in the null-space to satisfy some prior information (TV minimization), while the least square solution has no components in the null-space. Applying this method to Zubal phantom, the artifact generated by the least square solution is eliminated, and PSNR is 30.6112, 34.8751 and 38.8998 when the timing resolution is unused, 200ps and 100ps respectively and 16 views from $-45$ to $45$ are adopted.