MAXIMUM-LIKELIHOOD PARAMETER-ESTIMATION OF THE HARMONIC, EVANESCENT, AND PURELY INDETERMINISTIC COMPONENTS OF DISCRETE HOMOGENEOUS RANDOM-FIELDS

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 two-dimensional (2-D) homogeneous random field with mixed sp ectral distribution, On the basis of a 2-D Weld-like decomposition, th e field is represented as a sum of mutually orthogonal components of t hree types: purely indeterministic, harmonic, and evanescent, The sugg ested algorithm involves a two-stage procedure, In the first stage, we obtain a suboptimal initial estimate for the parameters of the spectr al support of the evanescent and harmonic components, In the second st age, we refine these initial estimates by iterative maximization of th e conditional likelihood of the observed data, which is expressed as a function of only the parameters of the spectral supports of the evane scent and harmonic components, The solution for the unknown spectral s upports of the harmonic and evanescent components reduces the problem of solving for the other unknown parameters of the field to linear lea st squares, The Cramer-Rao lower bound on the accuracy of jointly esti mating the parameters of the different components is derived, and it i s shown that the bounds on the purely indeterministic and deterministi c components are decoupled, Numerical evaluation of the bounds provide s some insight into the effects of various parameters on the achievabl e estimation accuracy, The performance of the maximum-likelihood algor ithm is illustrated by Monte Carlo simulations and is compared with th e Cramer-Rao bound.