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Let's say we are given measurements of some sort.

In many cases, it is safe to assume that noise is white noise, serially uncorrelated, and zero mean with some finite variance.

But in other cases, "red noise" exists such that the noise is correlated in time. What does one do in this case? Perhaps a Gaussian Process could be used?

What methods exist to characterize spatially-correlated noise?

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  • $\begingroup$ I'm not familiar with the term "red noise". The question sounds very broad. What would qualify as a correct answer? What research have you done? $\endgroup$ – D.W. May 10 '16 at 23:37
  • $\begingroup$ If by red noise you mean chirp signal - frequency changing, that interferes with your data, but the data itself is not chirping: there are techniques in meteorology that deals with it, but the best (if you can use it and it is not overkill) is using Fractional Fourier Transform - rotating space so the noise is linear, erasing it, rotating back and you have denoisef signal - at least audio or general signals are cleaned this way. Could you share more about your objective? $\endgroup$ – Evil May 11 '16 at 17:37
  • $\begingroup$ @D.W. I am thinking something like using inference with latent variable models $\endgroup$ – ShanZhengYang May 12 '16 at 19:11
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The basic approach is to model the noise as an appropriate stochastic process (aka random process). There's an entire subfield of statistics that has studied different kinds of stochastic processes, and they each have different properties. It would be too much to try to summarize that entire subfield in a single answer here.

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