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For high-quality synthetic aperture radar (SAR) processing, Doppler centroid ambiguity resolving is an essential procedure. A novel method for the resolution of Doppler ambiguity is presented which exploits the fact that, in the compressed azimuth time and range frequency domain, all targets span the same range frequency bandwidth and exhibit the same slope which is just proportional to the Doppler ambiguity number. The slope is removed by interpolation so that a simplified Radon transform can be applied. The use of entropy to find the maximum concentration of the Radon-transformed image can improve the robustness of the method. The proposed method directly gives a reliable estimate of the Doppler ambiguity number and is not affected by the azimuth partially covered targets. Experimental results show that the proposed method works well in medium- to high-contrast scenes.