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 example, it is of great interest to accurately estimate the intensities underlying the observed Poisson data. 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.