  This paper presents a statistical forward model for a Compton imaging system,
called Compton imager. This system, under development at the University of
Illinois Urbana Champaign, is a variant of Compton cameras with a single type
of sensors which can simultaneously act as scatterers and absorbers. This
imager is convenient for imaging situations requiring a wide field of view. The
proposed statistical forward model is then used to solve the inverse problem of
estimating the location and energy of point-like sources from observed data.
This inverse problem is formulated and solved in a Bayesian framework by using
a Metropolis within Gibbs algorithm for the estimation of the location, and an
expectation-maximization algorithm for the estimation of the energy. This
approach leads to more accurate estimation when compared with the deterministic
standard back-projection approach, with the additional benefit of uncertainty
quantification in the low photon imaging setting.
