Simulation Based Inference for PET Iterative Reconstruction

The analytical projector (system matrix) used in most PET reconstructions does not incorporate Compton scattering and other important physical effects that affect the process generating the PET data, which can lead to biases. In our work, we define the projector from the generative model of a Monte-Carlo simulator, which already encompasses many of these effects. Based on the simulator’s implicit distribution, we propose to learn a continuous analytic surrogate for the projector by using a neural density estimator. This avoids the discretization bottleneck associated with direct Monte-Carlo estimation of the PET system matrix, which leads to very high simulation cost. We compare our method with reconstructions using the classical projector, in which corrective terms are factored into a geometrically derived system matrix. Our experiments were carried out in the 2D setting, which enables smaller-scale testing.