Gaussian moments for noisy independent component analysis

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.