Are you speaking of Bridge cache?
Seems to me all you have to do is find the menus for setting the cache image size to full-size, then for clearing the cache. I haven't run Bridge for about 3 years now, so I don't remember exactly where those menus are, but they're there.
If I understand it correctly, if you have Bridge set to store full sized previews in cache, then it stores a JPG the full size of the image. If you zoom in to '100%/actual pixel size' with the Bridge viewer, then you do indeed see a representation of a full res of any particular image. But AFAIK you can only access the cache via Bridge. You can't go in with My Documents, and pull out a single JPG.
This also presupposes that the Bridge cache keeps a copy of deleted documents. I can just imagine the outcry on sites like this, if it was discovered that Bridge was that sloppy with cache file managment! So I suspect that you are out of luck, in that respect at least.
But you mention a back up, so the files were stored in two locations prior to being deleted? That doubles the chance of a file recovery program finding them. I'm guessing that you have tried the Recycle Bin, or whatever Mac systems use?
Cache flies are in hidden directory, address depends on OS, which you did not state.