MAXIMUM-LIKELIHOOD PARAMETER-ESTIMATION OF DISCRETE HOMOGENEOUS RANDOM-FIELDS WITH MIXED SPECTRAL DISTRIBUTIONS

This paper presents a maximum-likelihood solution to the general probl em of fitting a parametric model to observations from a single realiza tion of a real valued, 2-D, homogeneous random field with mixed spectr al distribution, On the basis of a 2-D Weld-like decomposition, the fi eld is represented as a sum of mutually orthogonal components of three types: purely indeterministic, harmonic, and evanescent, The proposed algorithm provides a complete solution to the joint estimation proble m of the random field components. By introducing appropriate parameter transformations, the highly nonlinear feast-squares problem that resu lts from the maximization of the likelihood function is transformed in to a separable least-squares problem, In this new problem, the solutio n for the unknown spectral supports of the harmonic and evanescent com ponents reduces the problem of solving for the transformed parameters of the field to linear least squares. Solution of the transformation e quations provides a complete solution of the field model parameter est imation problem.