Computational methods for hidden markov tree models : An application to wavelet trees
Durand J.B., Goncalves P., Guédon Y.. 2004. IEEE Transactions on Signal Processing, 52 (9) : p. 2551-2560.
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 : arbre; méthode statistique; modèle mathématique; modèle de simulation; algorithme
Article (a-revue à facteur d'impact)
Agents Cirad, auteurs de cette publication :
- Durand Jean-Baptiste — Bios / UMR AMAP