Re: Creating noise in the frequency domain?

"In Matlab, I create Gaussian noise images"

Why? Since you fail to mention "white," I will tell you anyway that
Gaussian white noise poorly models real image noise.

"I'm searching for a more efficient way"

Then just don't use Matlab. Duh!

"1. What is the frequency-domain-equivalent distribution of complex
numbers to *Gaussian* noise in the spatial domain? Is there any at
all?
2. Or vice versa: If I create random complex numbers drawn from a
*Gaussian* distribution in the frequency domain, what kind of luminance
distribution will result in the spatial domain?"

A linear transformation of Gaussian noise is Gaussian noise. An
orthogonal transformation of white noise (not necessarily Gaussian) is
white. An orthonormal transformation of zero mean noise (not necessarily
white or Gaussian) preserves variance.

"3. Second option: If I create random complex numbers drawn from a
*uniform* distribution in the frequency domain, what kind of luminance
distribution will result in the spatial domain?"

Assuming independently and identically distributed (i.i.d.) uniformly
distributed noise, the spatial domain noise will be white, almost
Gaussian, but possibly not even close to i.i.d.. Many statistical
operations depend on the i.i.d. condition. Gaussian plus white implies
independently distributed and independently distributed (plus some minor
conditions) implies white, but for non-Gaussian distributions, white does
not imply independently distributed.

"4. What constraints (max, min values) do I have to put upon the real and
imaginary components, if any?"

As I implied before, if your DFT is orthonormal, the variance of your
output will be the same as the variance of the input.

"5. Anything stupid else I missed?"

Why are you doing this?




.

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