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Eckart-Young-Mirsky just relates to approximation by low rank matrices, and it says that the error is best in terms of the operator norm, i.e. the action of the approximation is closest.

When you’re trying to compress an image you’re trying to optimize something quite different, so it is actually not too surprising.

Images have structure that can be exploited, and exploitable structure is everything. A Fibonacci spiral isn't going to have a nice low rank decomposition but it can be specified exactly (and thus reproduced exactly) in a small handful of bytes. EYM is a structure-free guarantee, so we can't expect it to show that SVD would perform better on the natural image manifold than would purpose-built algorithms.

Perceptual loss is different from mathematical RMSe loss. There has been a lot of work into making things that decompress into something mathematically completely different, but which to Mk1 Human Eyeball looks very similar.