Computational methods for hidden markov tree models : An application to wavelet trees

Durand Jean-Baptiste, Goncalves Paulo, Guédon Yann. 2004. Computational methods for hidden markov tree models : An application to wavelet trees. IEEE Transactions on Signal Processing, 52 (9) : 2551-2560.

https://doi.org/10.1109/TSP.2004.832006

Article de revue ; Article de revue à facteur d'impact

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Résumé : The hidden Markov tree models were introduced by Crouse et al. in 1998 for modeling nonindependent, non-Gaussian wavelet transform coefficients. In their paper, they developed the equivalent of the forward-backward algorithm for hidden Markov tree models and called it the "upward-downward algorithm." This algorithm is subject to the same numerical limitations as the forward-backward algorithm for hidden Markov chains (HMCs). In this paper, adapting the ideas of Devijver from 1985, we propose a new "upward-downward" algorithm, which is a true smoothing algorithm and is immune to numerical underflow. Furthermore, we propose a Viterbi-like algorithm for global restoration of the hidden state tree. The contribution of those algorithms as diagnosis tools is illustrated through the modeling of statistical dependencies between wavelet coefficients with a special emphasis on local regularity changes.

Mots-clés Agrovoc : arbre, méthode statistique, modèle mathématique, modèle de simulation

Mots-clés complémentaires : Algorithme

Classification Agris : U10 - Informatique, mathématiques et statistiques
K10 - Production forestière

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