We treat an image restoration problem with a Poisson noise chan- nel using aBayesian framework. The Poisson randomness might be appeared in observation oflow contrast object in the field of imaging. The noise observation is oftenhard to treat in a theo- retical analysis. In our formulation, we interpret theobservation through the Poisson noise channel as a likelihood, and evaluate thebound of it with a Gaussian function using a latent variable method. We thenintroduce a Gaussian Markov random field (GMRF) as the prior for the Bayesianapproach, and derive the posterior as a Gaussian distribution. The latentparameters in the likelihood and the hyperparameter in the GMRF prior could betreated as hid- den parameters, so that, we propose an algorithm to infer themin the expectation maximization (EM) framework using loopy beliefpropagation(LBP). We confirm the ability of our algorithm in the computersimulation, and compare it with the results of other im- age restorationframeworks.
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