Model parameter estimation for 2D noncausal Gauss-Markov random fields

An original procedure for estimating the model parameters of a noncausal Gauss-Markov random field (GMRF) from noisy observations is proposed. Starting from a suitable 'local' representation of the field and taking into account the symmetry property of the so-called 'potential fields' describing the GMRF, a linear equation system relating the model parameters to the (generally, nonstationary) 2D autocorrelation function (ACF) of the observed field is derived. Its solution for a known (or estimated) ACF directly gives the parameter estimates of the GMRF. The unknown variance of the eventually present observation noise can be also estimated jointly with the model parameters.