Kalman filtering in pairwise Markov trees

An important problem in multiresolution analysis of signals or images consists in estimating hidden random variables x={xs}s∈Sx={xs}s∈S from observed ones y={ys}s∈Sy={ys}s∈S. This is done classically in the context of hidden Markov trees (HMT). HMT have been extended recently to the more general context of pairwise Markov trees (PMT). In this note, we propose an adaptive filtering algorithm which is an extension to PMT of the Kalman filter (KF).