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Multiframe resolution enhancement ("superresolution") methods are becoming widely studied, but only a few procedures have been developed to work with compressed video, despite the fact that compression is a standard component of most image- and video-processing applications. One of these methods uses quantization-bound information to define convex sets and then employs a technique called "projections onto convex sets" (POCS) to estimate the original image. Another uses a discrete cosine transformation (DCT)-domain Bayesian estimator to enhance resolution in the presence of both quantization and additive noise. The latter approach is also capable of incorporating known source statistics and other reconstruction constraints to impose blocking artifact reduction and edge enhancement as part of the solution. We propose a spatial-domain Bayesian estimator that has advantages over both of these approaches.