Mode of posterior marginals with hierarchical models

This work takes place in the context of hierarchical stochastic models for the resolution of discrete inverse problems from low level vision. We investigate a new hybrid hierarchical structure: a Markov random field attached to the nodes of a truncated tree. It thus combines causal hierarchical prior on trees with a non-causal spatial prior at the coarsest level. We address the problem of computing posterior marginals with such a prior structure. This is performed using non-iterative two-sweep marginalizations on trees, combined with a low cost Gibbs sampler in between the two sweeps. Posterior marginals are thus obtained in a semi-iterative way. They are then used to infer unknown variables according to the IMPM estimator. This is illustrated by experiments on synthetic data and on multispectral satellite images