This all has been covered several times, but I have to work on my rating here :

While comparing original and processed (e.g. MP3-compressed) signal using spectrum analyser will reveal obvious shortcomings, it is far from being the whole story. We sometimes don't hear seemingly obvious differences; in other situations, the signal that looks almost perfect on the analyser will have, for example, phase distortions ruin the stereo image etc...

I think the only way to tell whether the signal processed in a particular way sounds indistinguishable from the the original is by listening (of course, in blind tests). (Then again, one can always tell vinyl from CD in blind listening test by hissing, clicking, shaved high freqs, lower dynamic range... :)
BTW, one can find interesting listening test rant here.

Regarding 'repairing' the signal, I understand that one can correct for differences in frequency or phase response between mastering and our own system, or 'undo' intentionally introduced known changes (Dolby, dynamic range compression). However, I think that, if we knew how to 'repair' poorly compressed MP3 signal, we could simply make better decoder....

Cheers!

Dragi "Bonzi" Raos
Zagreb, Croatia
#5196