Re: Creating noise in the frequency domain?

On May 24, 1:59 pm, "aruzinsky" <aruzin...@xxxxxxxxxxxxxxx
cathexis.com> wrote:
"Gaussian white noise is just a good approximation of many real-world
situations"

Not image noise. Image noise is almost always strongly correlated over a
space of several pixels. The Gaussian assumption isn't as bad because
linear transformations such as demosaicing make the noise more Gaussian
via the central limit theorem.

"and allows one to model them so they are easy to deal with
mathematically."

Except for the "and" part, yes.

"It is just one way of modeling white noise with a Gaussian amplitude
distribution. Using a Gaussian model does not say anything about the
spectral density of a signal; which means there could be other
distributions too that allow modeling a white noise signal"

Yes, but, when operations only involve correlation or spectral density,
there is no reason to model with another distribution because the
multivariate Gaussian distribution is completely determined by its first
two moments, mean and covariance.

Non-Gaussian distributions can be white and still contain information in
higher moments. In fact, it is possible to send messages in Non-Gaussian
white noise but not in Gaussian white noise.

e.g. "Poisson, Cauchy."

There is no such thing as "white Cauchy noise" because all of the moments
of the Cauchy distribution are infinite or undefined (take your pick). The
Cauchy distribution doesn't even have a mean. Also, the central limit
theorem doesn't apply to Cauchy random variables.


Oh yeah? Take a peek at this article:

http://nanolab.usc.edu/PDF%5CNanoLett3-1683.pdf

May be not in image processing practice, but either of those three
distributions can be used to model white noise. Just because you think
the realization is difficult, does not nullify the existence of a
concept.

In rest of the post, you just re-inforced my points with facts:
Gaussian is the choice when it comes to actual implementation: well
defined finite moments, convenience of central limit theorem.
Specifically in simple image processing applications where most people
find it easy to deal with on paper and with computer. Nothing new or
intellectually stimulating.

____
Pixel.To.Life.
Anonymous: Arrogance hinders learning and growth.


.

Relevant Pages

  • Re: Noise Source with Limiter ?
    ... And that ain't Gaussian. ... Nobody is disagreeing on this point. ... >> distribution of Gaussian noise. ... analog noise follow a Gaussian distribution, ...
    (sci.electronics.design)
  • Re: Does this have a flaw in de-biasing an entropy stream?
    ... "flat" distribution most users want. ... That depends on the noise source. ... to Poisson; some are Gaussian; some are binary ... If we define "noise" to mean a physical randomness source that has ...
    (sci.crypt)
  • Re: Frequency retrieval from noise
    ... distribution, one performs fourier transform to identify the ... noise, which means that the the spectrum of the noise is flat. ... I'm asking what are the peaks in the power spectrum of pure ... AWGN is gaussian in amplitude distribution, ...
    (sci.physics)
  • Re: Creating noise in the frequency domain?
    ... Gaussian white noise poorly models real image noise. ... What is the frequency-domain-equivalent distribution of complex ... distributed noise, the spatial domain noise will be white, almost ...
    (sci.image.processing)
  • Re: Creating noise in the frequency domain?
    ... Gaussian white noise poorly models real image noise. ... What is the frequency-domain-equivalent distribution of complex ... distributed noise, the spatial domain noise will be white, almost ...
    (sci.image.processing)