A Simple Information Theoretic Proof of the Maximum Entropy Property of Some Gaussian Random Fields

Abstract

A well known result of Burg and Kiinsch identifies a Gaussian Markov random 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 the maximum entropy theorem for random fields in n dimensions is presented in the special case that the given autocovariances are compatible with a unilateral autoregressive process. © 1994 IEEE