Top: optimized resize using photoshop (but no other tools)
Bottom: resize using PhotoZoom.
This is not a particularly impressive result compared to some.
Unfortunately, it works by working through the image with a progressive matrix pre-mulitply, in almost the same was as a filter, except that it works on a larger matrix so that it can take better account of (and be more sympathetic to) the image on a wider area.
It is still not possible to fill in missing writing or detail though. I am afraid that the badge can only be identified with greater resolution.
Kevin