[svantana]

I think the basic premise of this paper is wrong. Very few natural signals are bandlimited - if images were, they would be no need to store in high resolution, you could just upsample. Natural spectra tend to be pink (decaying ~3dB/octave), which can be explained by the fractal nature of our world (zoom in on details and you find more detail).

[wbl]

JPEG allocates very few bits to the higher frequency elements of the blocks, especially in chroma. https://vicente-gonzalez-ruiz.github.io/JPEG/#lossy-jpeg

[vlovich123]

Of course that says that our eyes (& more generally our sensory organs) are bandlimited which is what lossy signal compression algorithms exploit (similar to how MP3 throws away acoustic signals we can't hear or how even "lossless" is still only recorded at 44 kHz). And indeed any sensor has this problem and it's a physical limitation (e.g. there's only so much resolving power an optical sensor of a certain size can have for an object of a certain distance away which is why we can't see microscopic things and this is a limit from the physics of optics)

It says nothing about the underlying signal in nature. But of course we're building LLMs to interact with humans rather than to learn about signals in the true natural world that we might miss.

[wbl]

Any optical system will have a finite resolution.

[astrange]

That applies to individual samples. The eye gets around this by saccading (rapid movements) to get multiple samples. Also, you interact with your environment rather than passively sampling it, so if you want to look closer at something you can just do that.

Images aren't truly bandlimited because they contain sharp edges; if they were bandlimited you'd be happy to see an image upscaled with a Gaussian kernel, but instead it's obviously super blurry.

When we see an edge in a smaller image we "know" it's actually infinitely sharp. Another way to say this is that a single image of two people is fundamentally two "things", but we treat it as one unified "thing" mathematically. If all images came with segmentation data then we could do something smarter.

[pvillano]

"In optics, any optical instrument or system – a microscope, telescope, or camera – has a principal limit to its resolution due to the physics of diffraction." This might be what wbl is referring to.