Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging

Many important problems in engineering and science are well-modeled by Pois son processes. In many applications it is of great interest to accurately e stimate the intensities underlying observed Poisson data. In particular, th is work is motivated by photon-limited imaging problems. This paper studies a new Bayesian approach to Poisson intensity estimation based on the Haar wavelet transform. It is shown that the Haar transform provides a very natu ral and powerful framework for this problem. Using this framework, a novel multiscale Bayesian prior to model intensity functions is devised. The new prior leads to a simple Bayesian intensity estimation procedure. Furthermor e, we characterize the correlation behavior of the new prior and show that it has 1/f spectral characteristics. The new framework is applied to photon -limited image estimation, and its potential to improve nuclear medicine im aging is examined.