Abstract

Abstract—We propose a new model called a Pairwise Markov Chain (PMC), which generalizes the classical Hidden Markov Chain (HMC) model. The generalization, which allows one to model more complex situations, in particular implies that in PMC the hidden process is not necessarily a Markov process. However, PMC allows one to use the classical Bayesian restoration methods like Maximum A Posteriori (MAP), or Maximal Posterior Mode (MPM). So, akin to HMC, PMC allows one to restore hidden stochastic processes, with numerous applications to signal and image processing, such as speech recognition, image segmentation, and symbol detection or classification, among others. Furthermore, we propose an original method of parameter estimation, which generalizes the classical Iterative Conditional Estimation (ICE) valid for of classical hidden Markov chain model, and whose extension to possibly non-Gaussian and correlated noise is briefly treated. Some preliminary experiments validate the interest of the new model. Index Terms—Bayesian restoration, hidden data, image segmentation, iterative conditional estimation, hidden Markov chain, pairwise Markov chain, unsupervised classification. 1

Citations

6231	Maximum likelihood from incomplete data via the EM algorithm - Dempster, Laird - 1977
3011	Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images - Geman - 1984
1446	A new approach to linear filtering and prediction problems - Kalman - 1960
736	On the statistical analysis of dirty pictures - Besag - 1986
500	Probabilistic Networks and Expert Systems - Cowell, Dawid, et al. - 2003
475	Optimal Filtering - Anderson, Moore - 1979
176	From HMM‟s to segment models: a unified view of stochastic modeling for speech recognition - Ostendorf, Digalakis, et al. - 1996
139	Dynamic Linear Models with Markov-Switching - Kim - 1994
138	Multitarget-Multisensor Tracking: Principles and Techniques - Bar-Shalom, Li - 1995
114	Parametric hidden markov models for gesture recognition - Wilson, Bobick - 1999
93	Hidden markov processes - Ephraim, Merhav
85	Particle filters for state estimation of jump markov linear systems - Doucet, Gordon, et al.
79	Off-line handwritten word recognition using a hidden markov model type stochastic network - Chen, Kundu, et al. - 1994
74	Automatic segmentation of acoustic musical signals using hidden markov models - Raphael - 1999
52	Discrete Markov Image Modeling and Inference on the Quadtree - Laferté, Pérez, et al. - 2000
50	Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation - Giordana, Pieczynski - 1997
50	Kalman filtering with real-time applications - Chui, Chen - 2009
42	Joint parameter estimation and symbol detection for linear or nonlinear unknown channels - Kaleh, Vallet - 1994
37	Estimation of generalized mixtures and its application in image segmentation - Delignon - 1997
37	Sonar Image Segmentation Using an Unsupervised Hierarchical MRF Model - Mignotte, Collet, et al. - 2000
36	Explicit time correlation in hidden Markov models for speech recognition - Wellekens - 1987
35	A Bayesian approach to problems in stochastic estimation and control - Ho, Lee - 1964
30	Hidden markov chains and the analysis of genome structure - Churchill - 1992
27	An HMM-Based Approach for Off-Line Unconstrained Handwritten Word Modeling and Recognition - Sabourin, El-Yacoubi, et al. - 1999
27	Pairwise Markov Random Fields and segmentation of textured images - Pieczynski, Tebbache
26	Adaptive estimation and identification for discrete systems with Markov jump parameters - Tugnait - 1982
22	An equivalence of the EM and ICE algorithm for exponential family - Delmas - 1997
21	Signal and image segmentation using pairwise Markov chains - Derrode, Pieczynski - 2004
20	Triplet Markov chains in hidden signal restoration - Pieczynski, Hulard, et al. - 2002
17	Unsupervised non-stationary image segmentation using triplet Markov chains - Lanchantin, Pieczynski - 2004
16	Estimation of generalized mixture in the case of correlated sensors - Pieczynski, Bouvrais, et al. - 2000
16	Linear estimation - Kailath, Sayed, et al. - 2000
15	Unsupervised texture segmentation using multichannel decomposition and hidden Markov models - Chen, Kundu - 1995
12	The Viterbi algorithm - Fornay - 1973
12	On the use of Gibbs Markov chain models in the analysis of images based on second-order pairwise interactive distributions - Qian, Titterington - 1989
12	Kalman filtering using pairwise Gaussian models - Pieczynski, Desbouvries
11	Modelling non-Rayleigh speckle distribution in SAR images - Delignon, Pieczynski
11	A hidden semi-markov model with missing data and multiple observation sequences for mobility tracking - Yu, Kobayashi - 2003
10	Desbouvries, Kalman filtering in triplet Markov chains - Ait-el-Fquih, F
10	Particle filtering in pairwise and triplet Markov chains - Desbouvries, Pieczynski - 2003
9	Hidden hybrid Markov/semi-Markov chains - Guédon - 2005
9	Unsupervised restoration of hidden non stationary Markov chain using evidential priors - Lanchantin, Pieczynski
8	A maximization technique occuring in the statstical analysis of probabilistic functions of Markov chains - Baum, Petrie, et al. - 1970
8	Probabilistic Solution of Ill-Posed Problems in - Marroquin, Mitter, et al. - 1987
7	Kalman Filtering Techniques - Sorenson - 1966
5	Unsupervised signal restoration using Copulas and Pairwise Markov chains - Brunel, Pieczynski - 2003
5	Modèles de Markov triplet et filtrage de Kalman - Desbouvries, Pieczynski - 2003
5	Modèles et algorithmes pour l'analyse probabiliste des images - Pérez - 2003
4	Sur le choix de méthodes de segmentation statistique d’images - Salzenstein, Pieczynski - 1998
4	NonGaussian clutter modeling with generalized spherically invariant random vectors - Barnard, Weiner - 1996