Once information from the signal is lost it is gone forever and cannot be regained. That is scientific fact.
That is simultaneously true, and totally irrelevant.
Imagine I give you a black and white photograph of my garden, taken in summer. If you know something about the biology of grass, you will
easily be able to tell from that picture whether the grass was green or brown at the point the photograph was taken, despite the fact that there is no colour information in the picture at all. You can tell from the comparative brightness of the grass compared to other leaves, by whether or not there are bare patches of earth, lots of other things.
Starting from that black and white image you could therefore (given sufficient time, knowledge and computing power) reconstruct a
colour image which accurately reflects what the original scene would have looked like in colour, despite the fact that your starting point is in black and white. If you
didn't know anything at all about what colour grass normally is,
then it would be accurate to say that the colour information would be unrecoverable. But of course you
do know.
Now imagine capturing the sound of a violin as an arbitrarily good analogue signal, and then converting that into a red-book CD track. Again, information is lost - but, again, the recording itself is
not our only source of data. It's possible to study what happens when a very high-grade analogue signal is condensed into a CD. And using the combination of that knowledge
and the recording, you can recreate information that was lost during the recording process.
The aim should not be to construct a new analogue that exactly tracks the digital version. The aim should be to take the recording and extrapolate backwards to what the original sound
must have been to produce that digital recording.