  We treat an image restoration problem with a Poisson noise chan- nel using a
Bayesian framework. The Poisson randomness might be appeared in observation of
low contrast object in the field of imaging. The noise observation is often
hard to treat in a theo- retical analysis. In our formulation, we interpret the
observation through the Poisson noise channel as a likelihood, and evaluate the
bound of it with a Gaussian function using a latent variable method. We then
introduce a Gaussian Markov random field (GMRF) as the prior for the Bayesian
approach, and derive the posterior as a Gaussian distribution. The latent
parameters in the likelihood and the hyperparameter in the GMRF prior could be
treated as hid- den parameters, so that, we propose an algorithm to infer them
in the expectation maximization (EM) framework using loopy belief
propagation(LBP). We confirm the ability of our algorithm in the computer
simulation, and compare it with the results of other im- age restoration
frameworks.
