Title :
A simple information theoretic proof of the maximum entropy property of some Gaussian random fields
Author :
Politis, Dimitris N.
Author_Institution :
Dept. of Stat., Purdue Univ., West Lafayette, IN, USA
fDate :
11/1/1994 12:00:00 AM
Abstract :
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
Keywords :
Gaussian processes; Markov processes; autoregressive processes; covariance analysis; information theory; maximum entropy methods; Gaussian Markov random field; autocovariances; information theoretic proof; maximum entropy property; n-dimensional integer lattice; unilateral autoregressive process; Additive noise; Entropy; Filtering; Filters; Performance evaluation; Signal processing; Signal processing algorithms; Smoothing methods; Speech processing; White noise;
Journal_Title :
Image Processing, IEEE Transactions on
