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As an active microwave coherent imaging technology, synthetic aperture radar (SAR) images suffer from severe speckle noise and low-resolution problems due to the limitations of the imaging system, which cause difficulties in image interpretation and target detection. However, the existing SAR super-resolution (SR) methods usually reconstruct the images by a determined degradation model and hardly consider multiplicative speckle noise, meanwhile, most SR models are trained with synthetic datasets in which the low-resolution (LR) images are down-sampled from their high-resolution (HR) counterparts. These constraints cause a serious domain gap between the synthetic and real SAR images. To solve the above problems, this paper proposes an unsupervised blind SR method for SAR images by introducing SAR priors in a cycle-GAN framework. First, a learnable probabilistic degradation model combined with SAR noise priors was presented to satisfy various SAR images produced from different platforms. Then, a degradation model and a SR model in a unified cycle-GAN framework were trained simultaneously to learn the intrinsic relationship between HR–LR domains. The model was trained with real LR and HR SAR images instead of synthetic paired images to conquer the domain gap. Finally, experimental results on both synthetic and real SAR images demonstrated the high performance of the proposed method in terms of image quality and visual perception. Additionally, we found the proposed SR method demonstrates the tremendous potential for target detection tasks by reducing missed detection and false alarms significantly.