Identification of 2-D noncausal Gauss-Markov random fields

Parameter identification of multidimensional noncausal Markov random fields is an important paradigm in multidimensional signal processing and modeling, and the solutions to this problem are employed in many areas of image processing. An original procedure for estimating the model parameters of discrete-index 2-D noncausal Gauss-Markov random fields (GMRFs) 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