The restoration of an image sequence that is blurred before compression is considered. This describes many modern imaging systems that filter an image sequence during acquisition and then compress the result. It also describes the common scenario of preprocessing an image sequence with a digital filter prior to compression. No matter the source of degradation though, we seek to recover the high-frequency information without amplifying compression artifacts. The Bayesian framework is employed, and we present recovery algorithms that correspond to two common models for compression noise. Simulations then illustrate the efficacy of both techniques for the restoration of compressed video. Qualitative and quantitative results are presented.