We present a novel approach to image processing for optical detection of faint asteroids. Traditional methods of asteroid detection require observations in multiple frames taken over a period of time, but are limited by the signal-to-noise ratio in a single frame. Our approach is based on a velocity matched filter (VMF), which combines the signal from multiple frames in order to increase the aggregate SNR for dim objects. By generating a series of hypotheses about the apparent velocities of potential objects, we create a set of highly sensitive velocity-specific filters, the results of which are combined to achieve complete coverage of the search space. Each filter collapses a set of sidereal frames into a single frame through a shifted sum operation, thus aggregating the signal from the entire frameset and increasing SNR for objects matching the hypothesized velocity. We also present additional signal processing steps designed to filter out a variety of noise sources such as stars, spacecraft, and background gradients.