On the parameter estimation of the harmonic, evanescent and purely indeterministic components of homogeneous random fields

A maximum-likelihood (ML) estimation procedure for the parameters of homogeneous random fields is presented. On the basis of a 2D Wold-like decomposition, the random field is decomposed into a sum of mutually orthogonal components of three types: purely indeterministic, harmonic, and generalized evanescent. Because, in general, a homogeneous random field is characterized by a mixed spectral distribution, parameter estimation techniques which are solely based on spectral density estimators are not adequate. An algorithm which results in a complete parameter estimation for the purely indeterministic and harmonic components of the homogeneous random field and in estimates for the evanescent component frequencies is presented. The new ML method produces highly accurate estimates of these parameters