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A constructive proof is given for the existence and uniqueness of a two-dimensional discrete Markov random field which agrees with correlation values in a nearest neighbor array. The corresponding spectrum is the two-dimensional maximum entropy (ME) spectrum whose form was discovered by Burg. An iterative algorithm is developed for computing an approximation to this Markov spectrum for a regularly spaced array. The algorithm approximates the desired Markov correlation function by a truncated convolution power series (CPS) in an operator . The algorithm's performance is demonstrated on both simulated data and real noise data. The Markov spectral estimate can offer higher resolution than previously proposed spectral estimates.