"This is digital media file-focussed deduplication with special mathamatical techniques used to compress the supposedly uncompressable, JPEGs and the like."
Of course JPEGs can be recompressed. In fact virtually any media format file which uses lossy compression, like JPEGs, MP3s, MPEGs and so on can be reduced in size at the costs of quality. No special mathematical (or even mathamatical) techniques required. Alternatively, you can perform a file conversion to a more compact format and regenerate the original data type (rather naughtily, some software used to do this with non lossy files such as TIFFS - they would convert to JPEG before storing and regenerate the TIFF, thereby losing detail. That was important on medical archival systems for things like X-Rays where detail can literally be life-and-death).
However, what is utterly impossible is to do a "lossy" compression without being aware of the data type is. Do that and you have an unreadable file.