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The advent of deep learning has made a significant advance in ship detection in synthetic aperture radar (SAR) images. However, it is still challenging since the amount of labeled SAR samples for training is not sufficient. Moreover, SAR images are corrupted by speckle noise, making them complex and difficult to interpret even by human experts. In this letter, we propose a novel SAR ship detection framework that leverages label-rich electro-optical (EO) images for more plentiful feature representations, and delicately addresses the speckle noise in SAR images. To this end, we first introduce a multistage domain alignment module that reduces the distribution discrepancies between EO and SAR feature maps at local, global, and instance levels. This allows enriching SAR representations by gradually instilling cross-domain knowledge from a large-scale EO image dataset. We further design a blind-spot layer for feature extraction to suppress the influence of speckles. Experimental results on the high-resolution SAR images dataset (HRSID) show that our detection performance achieves average precision (AP) 5.5% better than the current state-of-the-arts that exploits SAR images only. Our method significantly improves the detection performance with higher speckle noises, demonstrating stronger robustness than the conventional methods.