Estimating the sky map in gamma-ray astronomy with a Compton telescope

The author offers a formal mathematical formulation of the problem of estimating the sky-map from low-level Compton telescope data. A structured approach is used to derive an iterative algorithm, termed the EM ML (expectation-maximization maximum-likelihood) algorithm, which yields the rigorously optimal estimate of the sky-map given the formulation. The EM ML algorithm converges to the global maximum of the likelihood function, resulting in a true maximum likelihood estimate of the sky map. The result is rigorously optimal given the Poisson assumption. Initial Monte Carlo simulations indicate that maximum likelihood estimation of the sky map may offer improved contrast and all ability to resolve multiple sources within a diffuse background. The computational requirements of the EM ML algorithm are, however, roughly 60 times greater than that of the event circle method