In this report, we investigate mathematical algorithms for image reconstruction in the context of positron emission tomography (a medical diagnosis technique). We first take inspiration from the physics of PET to design a mathematical model tailored to the problem. We think of positron emissions as an output of an indirectly observed Poisson process and formulate the link between the emissions and the scanner records through the Radon transform. This model allows us to express the image reconstruction in terms of a standard problem in statistical estimation from incomplete data. Then, we investigate different algorithms as well as stopping criterion, and compare their relative efficiency.