Free Access
Issue
Astron. Astrophys. Suppl. Ser.
Volume 137, Number 3, June II 1999
Page(s) 553 - 567
DOI https://doi.org/10.1051/aas:1999262
Published online 15 June 1999
DOI: 10.1051/aas:1999262

Astron. Astrophys. Suppl. Ser. 137, 553-567

Searching for non-gaussianity: Statistical tests

O. Forni and N. Aghanim

Send offprint request: N. Aghanim, aghanim@ias.fr

IAS-CNRS, Université Paris Sud, Bâtiment 121, F-91405 Orsay Cedex, France

Received February 3; accepted April 21, 1999

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.

Key words: methods: data analysis; statistical -- techniques: image processing


Copyright The European Southern Observatory (ESO)

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