Introduction

Independent Component Analysis (ICA) has recently become an important tool for modelling and understanding empirical datasets as it offers an elegant and practical methodology for blind source separation and deconvolution. It is seldom possible to observe a pure unadulterated signal. Instead most observations consist of a mixture of signals usually corrupted by noise, and frequently filtered. The signal processing community has devoted much attention to the problem of recovering the constituent sources from the convolutive mixture; ICA may be applied to this Blind Source Separation (BSS) problem to recover the sources. As the appellation independent suggests, recovery relies on the assumption that the constituent sources are mutually independent.

Finding a natural coordinate system is an essential first step in the analysis of empirical data. Principal component analysis (PCA) has, for many years, been used to find a set of basis vectors which are determined by the dataset itself. The principal components are orthogonal and projections of the data onto them are linearly decorrelated, properties which can be ensured by considering only the second order statistical characteristics of the data. ICA aims at a loftier goal: it seeks a transformation to coordinates in which the data are maximally statistically independent, not merely decorrelated.