Parameter estimation of two-dimensional moving average random fields

This paper considers the problem of estimating the parameters of two-dimensional (2-D) moving average random (MA) fields. We first address the problem of expressing the covariance matrix of nonsymmetrical half-plane, noncausal, and quarter-plane MA random fields in terms of the model parameters. Assuming the random field is Gaussian, we derive a closed-form expression for the Cramer-Rao lower bound (CRLB) on the error variance in jointly estimating the model parameters. A computationally efficient algorithm for estimating the parameters of the MA model is developed. The algorithm initially fits a 2-D autoregressive model to the observed field and then uses the estimated parameters to compute the MA model. A maximum-likelihood algorithm for estimating the MA model parameters is also presented. The performance of the proposed algorithms is illustrated by Monte-Carlo simulations and is compared with the Cramer-Rao bound.