A SIMPLE INFORMATION-THEORETIC PROOF OF THE MAXIMUM-ENTROPY PROPERTY OF SOME GAUSSIAN RANDOM-FIELDS

A well known result of Burg and Kunsch identifies a Gaussian Markov ra ndom field with autocovariances specified on a finite part L of the n- dimensional integer lattice, as the random field with maximum entropy among all random fields with same autocovariance values on L. In this correspondence, a simple information theoretic proof of a version of t he maximum entropy theorem for random fields in n dimensions is presen ted in the special case that the given autocovariances are compatible with a unilateral autoregressive process.