Re: Creating noise in the frequency domain?

On May 23, 5:01 pm, Matthias <ms.tre...@xxxxxxxxx> wrote:
In Matlab, I create Gaussian noise images that are subsequently
filtered in the frequency domain and then transformed back to the
spatial domain. I'm searching for a more efficient way to do this (as
I need lots of these images in little time). Just a try:

- Create a matrix with random complex numbers (random real and random
imaginary parts)
- perform some filtering
- normalize to mean luminance and contrast

So, basically, I skip the step of transforming into the frequency
domain, as noise is created directly in the freq. domain.

There are a few things about that which I do not perfectly get:
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?
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?
4. What constraints (max, min values) do I have to put upon the real
and imaginary components, if any?
5. Anything stupid else I missed?

Thanks in advance!

Matthias

Matthias,

I am just thinking outloud, so please ignore ideas that are
irrelevant.

Do you have a way to visualize the fourier transformed (real and
complex) images? Synthesizing a white-noise carrying 2D image, then
fourier transforming it, then visualizing it would already give you
some insight. You might have to shift the image components to have a
meaningful visualization of at least the real component. You know,
just as suppressing central portions from the fourier 2D image will
suppress corresponding frequency information from the spatial
counterpart, the 'whiteness' should be distributed randomly too on the
frequency domain image.

Interesting thought though. I found a slighty related paper here:
http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/7067/19060/00881298.pdf

Please keep us posted.

Pixel.To.Life.

.

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