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A new method for detecting moving targets in a synthetic aperture radar (SAR) image is presented. It involves segmenting a complex-valued SAR image into patches, focusing each patch separately, and measuring the sharpness increase in the focused patch. The algorithm is sensitive to azimuth velocities and is exquisitely sensitive to radial accelerations of the target, allowing it to detect motion in any direction. It is complementary to conventional Doppler-sensing moving target indicators, which can sense only the radial velocity of rapidly moving targets.