Actually, a restored copy (or even a digitized copy) would be a derived work. Derived works can be copyrighted independently of the foundation work, as long as some degree of artistic creativity was involved. If I digitally-restored an old film that was in the public domain, digitally-watermarked it, and you distributed unauthorized copies of it, I could most certainly sue you for infringement. I couldn't stop you from independently obtaining a copy of the original work and doing YOUR OWN restoration on it (and getting your own copyright), but I CAN stop you from using MY restored copy as your source.
Here are some other examples:
The original German text of Grimm's fairy tales: public domain
A translation of them (with a few artistic liberties) published long ago: public domain.
A new translation of them: the lines you changed are a derivative work & copyrighted. The lines that were unchanged from the original translation are public domain. The limits of how far someone could go republishing your translation with your own changes slightly paraphrased: anyone's guess, but likely to be messy.
You print an anthology of public domain works. I OCR them, and typeset & sell my own anthology. You MIGHT have a valid (if weak) copyright claim if my book had a 1:1 correspondence with yours (every story in one was in the other, in the same order, but without any interpretations/footnotes/etc added by you), but the more my book diverges from yours in form and content, the weaker your claim would be.
You print an anthology of public domain works. I scan each page, and use the images to publish my own anthology. You can absolutely sue me, because I violated the copyright on your "performance" of the original public-domain works.
I record myself playing a Beethoven fugue. You copy and sell verbatim copies: I can sue. The content itself is public domain, but my specific recorded performance of it is not. The process of recording, mixing, and editing added copyrightable value. On the other hand, if I performed it in a public place & you made YOUR OWN recording, I'd probably have no valid claim against you. And I absolutely couldn't stop you from performing the public-domain work YOURSELF, recording it, and releasing it on your own.