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

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.