A family of fixed-point algorithms for independent component analysis

Independent component analysis (ICA) is a statistical signal processing technique whose main applications are blind source separation, blind deconvolution, and feature extraction. Estimation of ICA is usually performed by optimizing a 'contrast' function based on higher-order cumulants. It is shown how almost any error function can be used to construct a contrast function to perform the ICA estimation. In particular, this means that one can use contrast functions that are robust against outliers. As a practical method for finding the relevant extrema of such contrast functions, a fixed-point iteration scheme is then introduced. The resulting algorithms are quite simple and converge fast and reliably. These algorithms also enable estimation of the independent components one-by-one, using a simple deflation scheme.