NASA is using a format for online files, called MRF (Meta Raster Format), which is claimed to deliver images ten times as fast as JPEG2000 from cloud services when used with a compression algorithm called LERC. LERC is under patent by Esri, which says the technique is especially suited for geospatial applications and makes the algorithm “freely available to the geospatial and earth sciences community.” An implementation of MRF from NASA is available on GitHub under the Apache license, and an implementation of LERC is on GitHub from Esri.
There’s another, much older format called MRF (Monochrome Recursive Format). It’s for images with a depth of one bit and has no connection to Meta Raster Format.
Update: Archiveteam.org added an entry for MRF less than half an hour after this post appeared, with a link back to here. Quick work!