Calculation of the Sensitivity Image in List-Mode Reconstruction for PET

List-mode image reconstruction is attracting renewed interest in emission tomography as the number of possible lines of response (LORs) in modern scanners becomes more than the number of detected events in one data set. One advantage of list-mode processing is that it eliminates the storage of empty sinogram bins. However, a single back projection of all LORs is still necessary for calculating the sensitivity image. Since the detection sensitivity is dependent on the object attenuation and detector efficiency, the sensitivity image must be computed for each study. Exact computation of the sensitivity image can be a daunting task for modern scanners with a huge number of LORs. Thus, some fast approximate calculation is desirable. Here we use theoretical results that we have derived to analyze a Monte Carlo based backprojection approach for calculating the sensitivity image. We derive expressions for the total number of LORs required in the backprojection and the sampling distribution. Computer simulations show that the nonuniform sampling schemes can reduce reconstruction artifact compared to the uniform sampling approach with the same computation cost