Multiscale Bayesian Restoration in Pairwise Markov Trees

Author

Desbouvries, François ; Lecomte, Jean

Author_Institution

GET/INT/CITI, Evry, France

Volume

50

Issue

8

fYear

2005

Firstpage

1185

Lastpage

1190

Abstract

An important problem in multiresolution analysis of signals and images consists in estimating continuous hidden random variables $\\bf x=\\bf x_s_s \\in cal S$ from observed ones $y = \\bf y_s _s \\in cal S$ . This is done classically in the context of hidden Markov trees (HMTs). In this note we deal with the recently introduced pairwise Markov trees (PMTs). We first show that PMTs are more general than HMTs. We then deal with the linear Gaussian case, and we extend from HMTs with independent noise (HMT-IN) to PMT a smoothing Kalman-like recursive estimation algorithm which was proposed by Chou , as well as an algorithm for computing the likelihood.

Keywords

Bayes methods; Gaussian processes; Kalman filters; hidden Markov models; pattern recognition; recursive estimation; smoothing methods; trees (mathematics); linear Gaussian method; multiresolution analysis; multiscale Bayesian restoration; pairwise hidden Markov trees; recursive estimation; smoothing Kalman filter; Bayesian methods; Feedback; Hidden Markov models; Image restoration; Multiresolution analysis; Recursive estimation; Signal processing; Signal processing algorithms; Signal restoration; Stochastic processes; Gaussian processes; hidden Markov trees (HMTs); multiscale algorithms; pairwise Markov trees (PMTs); recursive estimation;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2005.852552

Filename

1492562