Even sampling above the Nyquist rate, you can only reconstruct a signal perfectly if the samples themselves are perfectly precise - i.e., their binary or decima

Even sampling above the Nyquist rate, you can only reconstruct a signal perfectly if the samples themselves are perfectly precise - i.e., their binary or decimal representations have infinite digits. In practice the samples are truncated to a given sampling depth, and the difference is regarded as noise. In practice though, I think you could take your idea even further into the realm of lossy compression. If you're scanning newsprint for instance, the vast majority of the page is either 1) text in a known font or 2) images rendered through halftoning, that is a regular pattern of circles wih some finite range of radii. Conceivably a system intelligent enough to recognise and encode this information might even be considered a higher fidelity scan than a simple photo, as it will repair incidental defects from the printing process.