Computational methods for hidden Markov tree models-an application to wavelet trees

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 algor...

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Vydáno v:	IEEE transactions on signal processing Ročník 52; číslo 9; s. 2551 - 2560
Hlavní autoři:	Durand, J.-B., Goncalves, P., Guedon, Y.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.09.2004 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algorithms Applied sciences Computer Science Context modeling Equivalence Exact sciences and technology Hidden Markov models Image restoration Image segmentation Information, signal and communications theory Markov processes Mathematical methods Mathematical models Modeling and Simulation Regularity Signal processing algorithms Signal restoration Smoothing methods Telecommunications and information theory Trees Viterbi algorithm Wavelet Wavelet coefficients Wavelet transforms Change detection upward-downward algorithm wavelet decomposition Scaling law hidden Markov tree model Viterbi detection Wavelet transformation hidden state tree restoration Hidden Markov models scaling laws Diagnosis EM algorithm Computing method Signal detection
ISSN:	1053-587X, 1941-0476
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Popis
Shrnutí:	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.
Bibliografie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 content type line 23
ISSN:	1053-587X 1941-0476
DOI:	10.1109/TSP.2004.832006