Recover Frame Compression Lossiness from Many Similar Frames With many very similar frames of video that have been compressed with an unavoidably lossy encoding and available now as jpeg stills, are there available good mathematical techniques for recovering detail by considering multiple frames?  Certain areas of the image are of great interest and the artifacts there change from frame to frame.  Can they be cross-referenced to solve for higher detail?
The method to improve resolution by few frames is called Multi Image Super Resolution (As opposed to Single Image Super Resolution).
For compression artifacts you can look for JPEG Deblocking algorithms.