alt Hacker NewsDither 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.
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.