A novel approach for the problem of estimating the data model of independen
t component analysis (or blind source separation) in the presence of Gaussi
an noise is introduced. We define the Gaussian moments of a random variable
as the expectations of the Gaussian function (and some related functions)
with different scale parameters, and show how the Gaussian moments of a ran
dom variable can be estimated from noisy observations. This enables us to u
se Gaussian moments as one-unit contrast functions that have no asymptotic
bias even in the presence of noise, and that are robust against outliers, T
o implement the maximization of the contrast functions based on Gaussian mo
ments, a modification of the fixed-point (FastICA) algorithm is introduced.