How do I find the highest spatial frequency in an image?

(Former title: Given an upscaled image, how do I discover its original size?)

Let's say an image contains a signal. Let's say scaling up an image is oversampling the signal. Some kind of interpolation is used (GIMP offers linear, cubic, and sinc). So the solution lies in finding the minimum amount of开发者_StackOverflow中文版 points that, assuming a certain interpolation, are needed to to describe the signal with some very low error.

This sounds a lot like sound processing. Find the highest frequency component and you know the minimum sample rate you need.

Or something like that. Do I have the right idea? Where do I begin? Advice? Anything?

PS: If this has already been solved and is available a Photoshop plugin or whatever, do tell!

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Sorry - the question sounds like you want to find the highest spatial frequency in an image, and so how much an image could be REDUCED before losing any data?