  We propose a method to restore and to segment simultaneously images degraded
by a known point spread function (PSF) and additive white noise. For this
purpose, we propose a joint Bayesian estimation framework, where a family of
non-homogeneous Gauss-Markov fields with Potts region labels models are chosen
to serve as priors for images. Since neither the joint maximum a posteriori
estimator nor posterior mean one are tractable, the joint posterior law of the
image, its segmentation and all the hyper-parameters, is approximated by a
separable probability laws using the Variational Bayes technique. This yields a
known probability laws of the posterior with mutually dependent shaping
parameter, which aims to enhance the convergence speed of the estimator
compared to stochastic sampling based estimator. The main work is description
is given in [1], while technical details of the variational calculations are
presented in the current paper.
