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

  • Authors:

  • K. E. Timmermann;R. D. Nowak

  • Affiliations:

  • Dept. of Electr. Eng., Michigan State Univ., East Lansing, MI;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

Many important problems in engineering and science are well-modeled by Poisson processes. In many applications it is of great interest to accurately estimate the intensities underlying observed Poisson data. In particular, this 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 natural 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. Furthermore, 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 imaging is examined