Unsupervised edge-preserving image restoration via a saddle point approximation

This paper proposes a fast method to estimate the Gibbs hyperparameters of an MRF image model with explicit lines during the restoration process. It consists of a mixed-annealing algorithm for the maximization of the posterior distribution with respect to the image field, periodically interrupted to compute, via ML estimation, a new set of parameters. We first consider the weak membrane model and show that, by adopting a saddle point approximation for the partition function, these new parameters are defined as those that maximize the conditional prior distribution of the lines given the intensities, evaluated on the current estimate of the whole image field. In this way the computation of the expectations involved in the ML estimation can be performed by analytical summation over the binary line elements alone, with a strong reduction of the computational complexity. The approach can be extended to the general case of self-interacting line models, by substituting the analytical computations with a binary, short-range Gibbs sampler.