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The 2-D spectrum estimation is divided into the two consecutive 1-D spectrum estimations: a multichannel spectrum estimation in the "time" domain, and a scalar spectrum estimation in the "frequency" domain. The first is a purely parametric estimation, while the second is a mixture of parametric and nonparametric estimation. The maximum entropy method is used in each estimation in order to utilize the high resolution performance of the maximum entropy method, on the one hand, and to avoid the highly nonlinear nature of the maximum entropy method for 2-D problems, on the other hand. The estimate obtained by this procedure satisfies the covariance matching property and exhibits remarkably high resolution. A simplified version of the multichannel Levinson-Durbin algorithm is derived based on the special structure of the covariance data of homogeneous random fields. The related extendibility of the covariance array is discussed. It is shown that this method is particularly suitable for a class of random fields having some shift invariance.