Parameter estimation of two-dimensional moving average random fields: Algorithms and bounds

This paper considers the problem of estimating the parameters of two-dimensional moving average random fields. We first address the problem of expressing the covariance matrix of a moving average random field, in terms of the model parameters. Assuming the random field is Gaussian, we derive a closed form expression for the Cramer-Rao lower bound on the error variance in jointly estimating the model parameters. A computationally efficient algorithm for estimating the parameters of the moving average model is developed. The algorithm initially fits a two-dimensional autoregressive model to the observed field, then uses the estimated parameters to compute the moving average model.