Comment by giovannibonetti

I think there is a trade-off between spatial resolution and color depth. Dithering reduces the former to simulate increasing the latter.

Perhaps we can get a similar result by interpreting the original signal (after linearization) in a different way. It could represent (after normalization) the probability each pixel would be 1 or 0. That way, brighter areas would have more density of bright pixels, and darker areas would have more density of dark pixels.