Identification of 2D Noncausal Gauss-Markov Random Fields

An original procedure for estimating the model parameters of discrete-index 2-D noncausal Gauss-Markov random fields (GMRF’s) from noisy observations is proposed, valid for both finite and infinite lattices and for any kind of boundary conditions. Starting from a suitable ‘‘local’’ representation of the GMRF and taking into account the symmetry property of so-called field potentials, a linear equation set relating the model parameters to the 2-D autocorrelation function (known or estimated) of the observed field is derived. Its solution gives the parameter estimates of the GMRF together with the estimate of the (possibly unknown) variance of the observation noise.