Multiscale Bayesian estimation in Pairwise Markov Trees

An important problem in multiresolution analysis of signals and images consists in estimating hidden random variables (r.v.) x = {x_s}_s∈J from observed ones y = {y_s}_s∈J. This is done classically in the context of Hidden Markov Trees (HMT). In particular, a smoothing Kalman-like algorithm has been proposed by Chou et al. in the linear Gaussian case. In this paper we extend this algorithm to the more general framework of Pairwise Markov Trees (PMT).