  This paper proposes a non-Gaussian Markov field with a special feature: an
explicit partition function. To the best of our knowledge, this is an original
contribution. Moreover, the explicit expression of the partition function
enables the development of an unsupervised edge-preserving convex deconvolution
method. The method is fully Bayesian, and produces an estimate in the sense of
the posterior mean, numerically calculated by means of a Monte-Carlo Markov
Chain technique. The approach is particularly effective and the computational
practicability of the method is shown on a simple simulated example.
