I'm curious as to what types(s) of noise are not random, but it may be too complicated for this arena.
Not too complicated, but possibly off topic. I'll list a few quickly.
Pattern noise in the photosite array. Think of each photosite as starting from a repeatable value but that they don't all start exactly at "zero". Also sometime called Dark Signal Non-Uniformity (DSNU).
Photo Response Non-Uniformity (PRNU). Think of each photosite responding in a linear fashion when exposed to light but that some respond a little more or less than others.
Pattern noise in the multi-channel readout. Imagine you have 12 channels of readout and they don't all start at the same "zero". (BTW, bad cases cause banding.)
When performing sensors tests, these forms of noise can be effectively eliminated by subtracting two identical exposures leaving the truly random noise behind to be measured.