> And then, is it really impossible to develop an objective metric for the level of visible detail that is maintained? Is that really psychovisual and therefore subjective? Is there really nothing we can use from information theory to calculate the level of detail that emerges out of the noise? Or something based on maximum likelihood estimation?

I think you'll find something similar with audio, image, and video compression algorithms in general. The majority of these are explicitly designed to spend more bits on the parts that humans care about and fewer bits on the parts we won't notice. E.g. MP3 uses perceptual coding/masking: when there's loud sound at frequency f0 and a quieter sound at nearby f1=f0+(small delta f) most people won't hear the sound at f1 so the codec just throws it away. You'd be able to see the difference on a spectrogram but you wouldn't be able to hear it.