Hyperparameter estimation for incomplete data in Markov Random Field image restoration is investigated. Assuming linear dependence of energies wrt hyperparameters framework, we use a classical cumulant expansion technique for Maximum Likelihood estimation of hyperparameters of the prior, pixel regularization probability density function. The particular case where the prior potential is an homogenous function of pixels is fully analyzed. This approach is then extended to an explicit joint boundary-pixel process aimed to preserve discontinuities. A generalized stochastic gradient (GSG) algorithm with a fast sampling technique is devised aiming to achieve simultaneous hyperparameter estimation, pixel and boundary restoration. Image restoration performances of posterior mean performed during GSG convergence and of simulated annealing performed after GSG convergence are compared experimentally. Results and perspectives are given.
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