Energy-based scatter correction and energy dependent image reconstruction for PET scanners

In this paper we propose a comprehensive energy based scatter correction approach for PET. The detailed energy information that comes with the list-mode data, as well as the marked difference between the energy spectra of unscattered and scattered photons are used for the estimation of the scattered events distributions and inside the reconstruction algorithm to individualize the correction terms for each coincidence by taking into account the probability of each event to be a true, a scattered (or a random) given its position and energy information. The central piece of our approach is the two-dimensional detector energy response model represented as a linear combination of four components, each one representing a particular state a PET event can be found in: both photons unscattered, the second scattered while the first not, first photon scattered while the second not, and both photons scattered. For a set of events collected in the vicinity of a given line of response, the coefficient of each component is determined by applying a statistical estimator. As a result we obtain the number of scattered events that are in the given set. The model gives us also the variation of scatter fraction with the photon pair energies for that particular position in the data space.