Statistical methods offer a better modeling of the process of data
acquisition in PET. Some choices for these models will be reviewed, and
also some numerical algorithm to carry out the reconstruction. However,
statistical data fitting criterion leads to an ill-posed problem.
Several Bayesian penalization strategies had been proposed to date in
order to deal with this difficulty. Also Total Variation regularization
can be used to regularize this inverse problem in an edge-preserving
fashion.