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Dither loses information, so perfectly reversible might be an unreasonable goal. But I bet you could train or fine-tune a denoiser to do a really good job. This might make a cool paper, if there’s anything at all non-standard or surprising you discover along the way.

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When I mentioned "perfectly reversible", I meant the FFT itself. You run the FFT. You run the inverse FFT. Because the FFT was quantized to 0-255, you end up with a lot of stuff that doesn't belong in the image.

Gotcha, that’s true. There’s gradations of non-reversible. FFT in practice is still not perfectly reversible, even if you use floats and don’t quantize to 8-bit. Anyway, yeah, dither will be even more non-reversible, but given how good today’s denoisers are, I bet de-dither could be pretty good if it was attacked with the same level of rigor as denoise has been.

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