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A simple information theoretic proof of the maximum entropy property of some Gaussian random fields

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1 Author(s)
D. N. Politis ; Dept. of Stat., Purdue Univ., West Lafayette, IN, USA

A well known result of Burg (1967) and Kunsch (1981) 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. 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

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IEEE Transactions on Image Processing  (Volume:3 ,  Issue: 6 )