Simultaneous Image Restoration and Hyperparameter Estimation for Incomplete Data by a Cumulant Analysis

Marc Sigelle 1
1 PASTIS - Scene Analysis and Symbolic Image Processing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The purpose of this report is first to show the main properties of Gibbs distributions considered as exponential statistics on finite spaces, as well as their sampling and annealing properties. Moreover, the definition and use of their cumulant expansions enables to exhibit other important properties of such distributions. Last, we tackle the problem of hyperparameter estimation in an incomplete data frame for image restoration purposes. A detailed analysis of several joint restoration-estimation methods using generalized stochastic gradient algorithms is presented, requiring infinite, continuous configuration spaces. Using once again cumulant analysis and its relationship with Statistical Physics allows us to propose new algorithms and to extend them to an explicit boundary frame.
Type de document :
Rapport
RR-3249, INRIA. 1997
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Marc Sigelle. Simultaneous Image Restoration and Hyperparameter Estimation for Incomplete Data by a Cumulant Analysis. RR-3249, INRIA. 1997. 〈inria-00073440〉

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