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We present an approach that significantly increases the sensitivity for finding and tracking small and fast near-Earth asteroids (NEAs). This approach relies on a combined use of a new generation of high-speed cameras which allow short, high frame-rate exposures of moving objects, effectively "freezing" their motion, and a computationally enhanced implementation of the "shift-and-add" data processing technique that helps to improve the signal-to-noise ratio (SNR) for detection of NEAs. The SNR of a single short exposure of a dim NEA is insufficient to detect it in one frame, but by computationally searching for an appropriate velocity vector, shifting successive frames relative to each other and then co-adding the shifted frames in post-processing, we synthetically create a long-exposure image as if the telescope were tracking the object. This approach, which we call "synthetic tracking," enhances the familiar shift-and-add technique with the ability to do a wide blind search, detect, and track dim and fast-moving NEAs in near real time. We discuss also how synthetic tracking improves the astrometry of fast-moving NEAs. We apply this technique to observations of two known asteroids conducted on the Palomar 200 inch telescope and demonstrate improved SNR and 10 fold improvement of astrometric precision over the traditional long-exposure approach. In the past 5 yr, about 150 NEAs with absolute magnitudes H = 28 (10 m in size) or fainter have been discovered. With an upgraded version of our camera and a field of view of (28 arcmin)2 on the Palomar 200 inch telescope, synthetic tracking could allow detecting up to 180 such objects per night, including very small NEAs with sizes down to 7 m. © 2014. The American Astronomical Society. All rights reserved..