Multiscale Bayesian restoration in pairwise Markov trees

An important problem in multiresolution analysis of signals and images consists in estimating continuous hidden random variables x = {x_S}_SεS from observed ones y = {y_S}_SεS. 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 et al., as well as an algorithm for computing the likelihood.