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

Compton telescopes represent an effective design for γ-ray astronomy in the 1-30 MeV range. However, the complexity of the system response to incident γ-rays has restricted the formulation of optimal methods for processing the data. Since data is only acquired at considerable expense and difficulty a significant investment in both algorithm development and computer processing time are warranted. Current methods for processing low level data form the sky map as either the sum or product of the probabilities that each recorded γ-ray originated from within an area of the sky map. Instead, we model the unknown sky map itself as the means of a Poisson process generating the γ-ray recorded by the telescope. In this paper the authors formulate the probability density function of the data conditioned upon the sky map and derive an iterative algorithm for estimating the sky map by the method of maximum likelihood