Ke. Timmermann et Rd. Nowak, Multiscale modeling and estimation of Poisson processes with application to photon-limited imaging, IEEE INFO T, 45(3), 1999, pp. 846-862
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.