Thursday, November 19, 1998
4:30 - 5:30 PM
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. This talk discusses 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 probability model for intensity functions is devised. The new prior leads to a simple, Bayesian intensity estimation procedure. Furthermore, the correlation function of the new prior is shown to have 1/f spectral characteristics, making it especially well suited to image modeling. Applications of the new framework to photon-limited image estimation, and nuclear medicine imaging in particular, are discussed.
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