Bayesian Estimation for Homogeneous and Inhomogeneous Gaussian Random Fields

This paper investigates Bayesian estimation for Gaussian Markov random fields. In particular, a new class of compound model is proposed which describes the observed intensities using an inhomogeneous model and the degree of spatial variation described by a second random field. The coupled Markov random fields are used as prior distributions, and combined with Gaussian noise models to produce posterior distributions on which estimation is based. All model parameters are estimated, in a fully Bayesian setting, using the Metropolis-Hasting algorithm. The full posterior estimation procedures are illustrated and compared using various artificial examples. For these examples the inhomogeneous model performs very favorably when compared to the homogeneous model, allowing differential degrees of smoothing and varying local textures.