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Surveys the field of super resolution (SR) processing for compressed video. The introduction of motion vectors, compression noise, and additional redundancies within the image sequence makes this problem fertile ground for novel processing methods. In conducting this survey, though, we develop and present all techniques within the Bayesian framework. This adds consistency to the presentation and facilitates comparison between the different methods. The article is organized as follows. We define the acquisition system utilized by the surveyed procedures. Then we formulate the HR problem within the Bayesian framework and survey models for the acquisition and compression systems. This requires consideration of both the motion vectors and transform coefficients within the compressed bit stream. We survey models for the original HR image intensities and displacement values. We discuss solutions for the SR problem and provide examples of several approaches.