  We present an approach that significantly increases the sensitivity for
finding and tracking small and fast near Earth asteroids (NEA's). 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 NEA's. 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 NEA's in near real
time. We discuss also how synthetic tracking improves the astrometry of fast
moving NEA's. 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 years, about 150 NEA's 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.
