Multiscale Bayesian estimation of Poisson intensities

Many important phenomena in science and engineering are! well modeled as Poisson processes. In some applications, photon imaging, for ea:ample, it is of great interest to accurately estimate the intensities underlying the observed Poisson data. In this paper we present a novel multiscale Bayesian approach to this problem. We show that Bayesian estimation in a multiresolution framework provides a very natural and powerful method for estimating the underlying intensity. Within this framework, we devise Bayesian priors suitable for a wide class of real-world processes. The resulting Bayes-optimal estimators have a simple and elegant form that leads to an efficient implementation.