Comment by CyberRabbi
5 years ago
Another way to think of dither (that may only make sense to people with a signals background) is that it linearizes the error introduced by the quantization step (which is a non-linear process). This has a bunch of conceptual implications (like elimination of error harmonics being natural consequence) but maybe most importantly allows you to continue using linear analysis tools and techniques in systems with a quantization filter.
This thesis on noise shaping and dither http://uwspace.uwaterloo.ca/bitstream/10012/3867/1/thesis.pd... is an excellent mathematical treatment of the subject.
Very cool paper. Something that bothers me is that the Floyd-steinberg error diffusion without dithering looks superior than the version with the dithering. I think this demonstrates that perceptible patterns in the error (non-linear) don’t always look so bad.
One thing I've found (admittedly with audio) is that you can usually get away with less dither power than is needed to completely linearize the error, at the cost of some harmonics for pathological signals which still ends up being less noticeable than the higher power dither noise.
I expect something similar to apply to images.
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