# What is a non-linear gaussian?

1. Oct 6, 2009

### stabu

Googling this has only given me fairly detailed scientific papers and wikipedia (unusually) doesn't come up. Does anybody have a cheap and cheerful definition?
Deducing these terms literally is not risk-free, but I suppose it involves a Gaussian probability distribution N(mu,sigma) where mu and sigma (may be one, may be both) do not vary linearly with a certain parameter .. potentially, time.

Still, that leaves it too general ... I expect it may implicitly refer to some methods. Certainly, image filtering seems to be one of its more salient applications.

However, I have to admit that I'm not very happy with usage of the term "non-linear". For me it has always meant "not specifically linear", which only implies to me a more general case.

Anyhow, any clues welcome, thank you.

2. Oct 6, 2009

### bpet

What's a linear gaussian, and is a noun missing?

3. Oct 7, 2009

### stabu

thanks for the question ...he,he.

I can answer a little and say that there is always something missing from any title or label. The missing bit is usually found implicitly n the background or context.

A Gaussian ... well the noun is implicit. It could be a distribution, but also a process. The linearity or non-linearity must refer to the variables that define the Gaussian, and how they change with reference to some parameter, which can often be time t.

As you have asked off somebody who also originally asked a question, this thread can quickly descend into the blind leading the blind, and end up with a bunch of mush as its result.

However, I am surmising so may be I'm not miles away. A Gaussian can also easily be a process which may be an iterated application of the normal probability distribution, where each time the mean and variance ($\sigma^2$ not "sigma" as I said previously) vary each time the iteration is applied. That variation may be linear or non-linear.

I think I'll run off now and check out the Image filtering application, maybe that's the best way to find out.