Joint Image Restoration and Segmentation using Gauss-Markov-Potts Prior Models and Variational Bayesian Computation: Technical Details

摘要

We propose a method to restore and to segment simultaneously images degradedby a known point spread function (PSF) and additive white noise. For thispurpose, we propose a joint Bayesian estimation framework, where a family ofnon-homogeneous Gauss-Markov fields with Potts region labels models are chosento serve as priors for images. Since neither the joint maximum a posterioriestimator nor posterior mean one are tractable, the joint posterior law of theimage, its segmentation and all the hyper-parameters, is approximated by aseparable probability laws using the Variational Bayes technique. This yields aknown probability laws of the posterior with mutually dependent shapingparameter, which aims to enhance the convergence speed of the estimatorcompared to stochastic sampling based estimator. The main work is descriptionis given in [1], while technical details of the variational calculations arepresented in the current paper.