Does the inequality kill super-resolution?
Many images, one measurement
Every candidate below downsamples to exactly the same low-resolution image — not approximately, not visually, but byte for byte. Given only that measurement, no algorithm can possibly tell you which one you were looking at. So the honest question is not "which is correct?" but "which is most likely?".
This is all the evidence there is. Each of its pixels is the average of an 8×8 block of the original — the same box average a sensor, a mipmap or a video downscale performs.
A super-resolution network never escapes the ambiguity below. What it does is rank the consistent candidates using regularities it absorbed from its training set — and then commit to the top one, confidently, whether or not it is right.
Paint anything. Then press the button: it redistributes the values within each 8×8 block at random while holding every block mean exactly fixed. The picture on the left changes completely; the measurement on the right does not move by a single unit. That is the null space of the downsampling operator, and it is where every super-resolution method is forced to guess.
The inequality is true, and super-resolution is still useful. Both statements hold, because they are about different things. Downsampling is a many-to-one map: an 8×8 block of 256-level pixels has astronomically many arrangements that share a mean, and averaging discards every distinction between them. Nothing recovers what was thrown away. The data processing inequality is not a technicality to be engineered around — it is a proof.
What a network adds is not information about your image. It is information about images in general. Of all the candidates consistent with the measurement, the overwhelming majority are noise; real photographs occupy a vanishingly thin sliver of that space. A model trained on millions of photographs learns the shape of that sliver, and picks the consistent candidate that lies inside it. That is a prior, and it was gathered at training time, long before it ever saw your image.
Which is exactly why it can be confidently wrong. Upscale a face and you get a plausible face — not that person's face. Upscale a number plate and you get plausible characters, which is precisely what makes the forensic version of this scene dangerous rather than merely inaccurate. The output is a sample from what the model believes, constrained by what was measured. Both halves of that sentence matter.