Noncausal Gauss Markov random fields: parameter structure and estimation

The parameter structure of noncausal homogeneous Gauss Markov random fields (GMRF) defined on finite lattices is studied. For first-order (nearest neighbor) and a special class of second-order fields, we provide a complete characterization of the parameter space and a fast implementation of the maximum likelihood (ML) estimator of the field parameters. For general higher order fields, tight bounds for the parameter space are presented and an efficient procedure for ML estimation is described. Experimental results illustrate the application of the approach presented and the viability of the present method in fitting noncausal models to 2-D data.