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This paper proposes a novel approach for Synthetic Aperture Radar (SAR) image segmentation by incorporating known statistical properties of SAR into deep learning models. We generate synthetic data using the Generalized Gamma distribution, modify the U-Net architecture to encompass statistical moments, and employ stochastic distance losses for improved segmentation performance. Evaluation against traditional methods will reveal the potential of this approach to advance SAR image analysis, with broader applications in environmental monitoring and general image segmentation tasks.