The questiion is, what was "lost" and what was "diminished". It's a mistake to assume that nothing above a certain frequency (5,000 cps for instance) or below a certain frequency (200 cps for instance) was recorded in, say, an acoustic recording or over long-distance landline transmission (as in certain broadcast recordings). It often is not a matter of hitting a brick wall, or a block filter, but rather of a sharp rolloff--something is there, but not at a very audible level, particularly if there is noise present. This can be amplified to a certain extent, but as of now if you go very far you will be amplifying distortion as well. The trick will be developing software that can discern--and eliminate--what is distortion.
As far as noise goes, the best thing to do is to find copies of the recording that aren't noisy in the first place. In many cases original stampers exist for commercial 78s and vinyl copies can be made to work from; this has been going on since the earliest LP transfers of 78s. There were also, especially in the US from about 1930-1941, 78s made specifically for electrical pickups from low-noise materials rather than with the abrasives added for acoustic pickups, where the records were made to grind down metal or fiber needles. You could order "Z pressings" (so-called because they have a tiny raised Z in the inner land of the disc, next to the label) from RCA, and Columbia had a line of pressings in a blue material; both play quietly if you can find copies in good shape. This includes custom re-pressing of many acoustic titles.
Noise reduction has gotten very, very good over the past 30 years. Computer logic is very advanced in distinguishing bits of noise from music and filleting the noise out from in between the soundwaves of the music, extrapolating if necessary from the frequencies surrounding the noise. The best, however, still requires close moment-by-moment oversight. It's not enough to just upload a sound file of the whole recording and click a box from a drop-down menu.
