We demonstrate a signal processing concept for imaging the sky at millisecond rates with radio interferometers. The Pocket Correlator (PoCo) correlates the signals from multiple elements of a radio interferometer fast enough to image brief, dispersed pulses. By the nature of interferometry, a millisecond correlator functions like a large, single-dish telescope, but with improved survey speed, spatial localization, calibration, and interference rejection. To test the concept, we installed PoCo at the Allen Telescope Array (ATA) to search for dispersed pulses from the Crab pulsar, B0329+54, and M31 using total-power, visibility-based, and image-plane techniques. In 1.7 hours of observing, PoCo detected 191 giant pulses from the Crab pulsar brighter than a typical 5 sigma sensitivity limit of 60 Jy over pulse widths of 3 milliseconds. Roughly 40% of pulses from pulsar B0329+54 were detected by using novel visibility-based techniques. Observations of M31 constrain the rate of pulses brighter than 190 Jy in a three degree region surrounding the galaxy to <4.3/hr. We calculate the computational demand of various visibility-based pulse search algorithms and demonstrate how compute clusters can help meet this demand. Larger implementations of the fast imaging concept will conduct blind searches for millisecond pulses in our Galaxy and beyond, providing a valuable probe of the interstellar/intergalactic media, discovering new kinds of radio transients, and localizing them to constrain models of their origin.
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