In this paper, we proposed to investigate unsupervised anomaly detection in Synthetic Aperture Radar (SAR) images. Our approach considers anomalies as abnormal patterns that deviate from their surroundings but without any prior knowledge of their characteristics. In the literature, most model-based algorithms face three main issues. First, the speckle noise corrupts the image and potentially leads to numerous false detections. Second, statistical approaches may exhibit deficiencies in modeling spatial correlation in SAR images. Finally, neural networks based on supervised learning approaches are not recommended due to the lack of annotated SAR data, notably for the class of abnormal patterns. Our proposed method aims to address these issues through a self-supervised algorithm. The speckle is first removed through the deep learning SAR2SAR algorithm. Then, an adversarial autoencoder is trained to reconstruct an anomaly-free SAR image. Finally, a change detection processing step is applied between the input and the output to detect anomalies. Experiments are performed to show the advantages of our method compared to the conventional Reed-Xiaoli algorithm, highlighting the importance of an efficient despeckling pre-processing step.