PET reconstruction using a generative model based on physical simulation

The Radon projector used in most PET reconstructions does not incorporate Compton scattering and other important physical effects that affect the PET process, resulting in biases despite the use of corrections. In our work, we define the projector from the generative model of a Monte-Carlo simulator, which encompasses many of these effects, including scattering. From the implicit simulator model, we propose to learn a continuous surrogate of the projector using a neural density estimator, thus avoiding the discretization bottleneck and lowering simulation cost. Our work is carried out in the two-dimensional PET configuration and compared with the reconstruction using the Radon projector, in which corrective terms are factored into the PET matrix. We observed reduced noise at match bias with our method, illustrating the interest of this simulation-based approach.The principal objective of this work is to establish a proof of concept for the SBI approach in PET.