What a restoration can recover, what it supplies from a prior, and how to tell.
3 May 2027
What a restoration can recover, what it supplies from a prior, and how to tell.
Week 4 asked whether the evidence on a single output could tell two histories apart. This week asks a related question about a different kind of claim: when someone shows you a “before” and an “after” and says the after is a recovery of the before’s lost detail, what would actually verify that — and what would only make it look verified?
Three things that are not the same claim#
Plausible. The restored image looks like a coherent photograph — nothing about it screams “wrong.” This is the weakest claim a restoration can make, and the easiest one to satisfy: a generative method only has to produce some image consistent with the low-resolution input, not the specific image that was actually there.
Verified. The restored value at a specific, named location matches a retained source you can check it against. This is a strong claim, but it requires exactly what a real restoration usually does not have: the original.
Uncertain, not fabricated. Some regions were never at risk. A large flat area that a degradation step averaged and a restoration step interpolated will usually still look flat and match — but that match tells you nothing about the restoration method’s actual power, because a flat area survives almost any degradation and almost any restoration. Calling every newly computed pixel “invented” ignores this: some of what a restoration outputs is trivially safe, some is a genuine guess, and only checking against retained evidence tells you which.
The pack’s own result, stated plainly#
This week’s pack degrades an 8x8 synthetic tone chart by averaging every 2x2 block, then restores it with bilinear interpolation — a named, ordinary upsampling method, not a generative model. Checked against the retained source at six named locations: two features inside already-uniform blocks matched (uninformative — nothing was lost there to recover), and of four features inside blocks that had genuine internal variation, one matched and three did not. One correct match out of four genuine recovery attempts, in this one specimen, with this one method, is not a recovery rate — it is what this pack’s own arithmetic produced, and the lecture is not claiming it generalises.
What a documented failure actually shows#
PULSE (Menon et al., CVPR 2020) searches a generative model’s space of plausible faces for one that downsamples to match a blurry input — it does not, and by its own design cannot, reconstruct the specific person’s true appearance. When researchers ran a pixelated photo of Barack Obama through it, the output had white skin and blue eyes (Quach, The Register, 2020) — verifiably wrong, because a real photograph of Obama exists to check against. That is the same structure as this week’s pack, at much higher stakes: a plausible output, checked against a retained source, found unsupported. The correct general lesson is not “generative restoration invents things” as a blanket rule — it is that plausibility was never evidence of correctness, and checking requires exactly the retained source that a real restoration claim, unlike this pack’s, usually cannot supply.
Before Wednesday#
Download the pack. Read pixels.csv before you look at restored.svg, and
write down which of the six features you expect to match before you check.
Teaching team
- Dr Wren Halloway — convenor