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An innovative constant false alarm rate (CFAR) algorithm was studied for ship detection using synthetic aperture radar (SAR) images of the sea. Two advances were achieved. An alpha-stable distribution rather than a traditional Weibull or -distribution was used to model the distribution of sea clutter. The distribution of sea clutter in a SAR image was typically heterogeneous, caused mainly by variable wind and current conditions. Image segmentation was carried out to improve the homogeneity of the distribution in each subimage or region. In comparison with ship detection using the CFAR algorithms based on the Weibull or K -distribution, our algorithm detected the most number of ships with the smallest number of false alarms.