Fast ICA for noisy data using Gaussian moments

A novel approach for the problem of estimating the data model of independent component analysis (or blind source separation) in the presence of Gaussian 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 random variable can be estimated from noisy observations. This enables us to use gaussian moments as one-unit contrast functions that have no asymptotic bias even in the presence of noise, and that are robust against outliers. To implement efficiently the maximization of the contrast functions based on Gaussian moments, a modification of our FastICA algorithm is introduced.