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Lognormal random fields with multiplicative spatial interaction are proposed for modeling radar image intensity. Two particular classes of two-dimensional (2-D) lognormal random fields are introduced: multiplicative autoregressive (MAR), and multiplicative Mnrkov random fields (MMRF). The MAR and MMRF models are formulated as invertible point-transformations of Gaussian autoregressive and Gaussian Markov random fields (GMRF) and therefore possess many desirable properties. Least squares and maximum likelihood estimates for random-field parameters are presented, a decision rule is developed for selecting model order and transformations to normality as well, and techniques for synthesizing 2-D lognormal random fields are provided. Several Seasat synthetic aperture radar (SAR) images were tested using the decision rule developed in this paper and using the Kolmogorov-Smirnov (K-S) goodness-of-fit test. With both tests they were found to possess a good fit to lognormal statistics. MAR and MMRF models were fit to Seasat SAR images, and then the models were used to generate synthetic images that closely resemble the original SAR images both visually and in their variograms. This demonstrates the generality and appropriateness of the MAR and MMRF models for radar imagery.