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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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 52; no. 9; pp. 2551 - 2560
Main Authors: Durand, J.-B., Goncalves, P., Guedon, Y.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.09.2004
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2004.832006