In blind image restoration the parameters of the imaging system are unknown, and must be estimated along with the restored image. Assuming that the images are piecewise smooth, the most part of the information needed for the estimation of the degradation parameters is expected to be located across the discontinuity and hence a better estimation of the paper we adopt a fully Bayesian approach which enables the joint MAP estimation of the image field and the ML estimations of the degradation parameters and the MRF hyperparameters. Owing to the presence of an explicit, binary line process, we exploit suitable approximations to greatly reduce the computational cost of the method. In particular, we employ a mixed-annealing algorithm for the estimation of the intensity and the line fields, periodically interrupted for updating the degradation parameters and the hyperparameters, based on the current estimate of the image field. The degradation parameters are updated by solving a least square problem of very small size. To update the hyperparameters we exploit MCMC techniques and saddle point approximations to reduce the computation of expectations to low cost time averages over binary variables only.
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