An information-theoretic derivation of the 2-D maximum entropy spectrum

It is known that the spectrum of the two-dimensional (2-D) stochastic process maximizing the entropy rate, among stationary Gaussian processes subject to a finite number of autocorrelation constraints, is that of the 2-D autoregressive (AR) process. We consider a 2-D entropy maximization problem, in which stationarity and normality are not assumed. The burden of proof is then shifted from the previous focus on the calculus of variations and complex analysis to a string of information-theoretic relationships.