Signal restoration using hidden Markov chains with copulas

Nicolas Brunel (1, 2, 3) , Wojciech Pieczynski (4, 1, 2, 3)

1 TSP - CITI - Communications, Images et Traitement de l'Information
2 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
3 CNRS - Centre National de la Recherche Scientifique
4 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications

This paper deals with the statistical restoration of hidden discrete signals, extending the classical methodology based on hidden Markov chains. The aim is to take into account the hidden signal and complex relationships between the noises which can be from different parametric models, non-independent, and of class-varying nature. We discuss some possibilities of managing it using copulas. Further, we propose a parameter estimation method and apply resulting unsupervised restoration methods in variety of situations. It is also validated by experiments performed in supervised and unsupervised context

Mots clés: Hidden Markov chains; Pairwise Markov chains; Triplet Markov chains; Copulas; Parameter estimation; Bayesian restoration; Stochastic expectation-maximization; Statistical image segmentation

Domaines: Traitement du signal et de l'image [eess.SP]

Nicolas Brunel, Wojciech Pieczynski. Signal restoration using hidden Markov chains with copulas. Signal Processing, 2005, 85 (12), pp.2304 - 2315. ⟨10.1016/j.sigpro.2005.01.018⟩. ⟨hal-01347782⟩