Searching for non-gaussianity: Statistical tests
O. Forni, N. Aghanim;
AaAS, 1999, 137, 553
ABSTRACT:Non-gaussianity represents the statistical signature of physical processes such as turbulence.
It can also be used as a powerful tool to
discriminate between competing cosmological scenarios.
A canonical analysis of
non-gaussianity is based on the study of the distribution of the signal in the real (or
direct) space (e.g.
brightness, temperature).
This work presents an image
processing method in which we propose statistical tests to indicate and quantify
the non-Gaussian nature of a signal.
Our method is based on a wavelet
analysis of a signal.
Because the temperature or brightness distribution is a
rather weak discriminator, the search for the statistical signature of
non-gaussianity relies on the study of the coefficient distribution of an image in the
wavelet decomposition basis which is much more sensitive.
We develop two
statistical tests for non-gaussianity.
In order to test their reliability, we
apply them to sets of test maps representing a combination of Gaussian and
non-Gaussian signals.
We deliberately choose a signal with a weak non-Gaussian
signature and we find that such a non-Gaussian signature is easily detected using
our statistical discriminators.
In a second paper, we apply the tests in a
cosmological context.
KEYWORDS: methods: data analysis, statistical, techniques: image processing
CODE: forni99