Independent Component Analysis: Concepts and Tools

In this talk, we describe briefly the main idea behind Independent Component Analysis (ICA), its links with Blind Source Separation, Principal Component Analysis and Projection Pursuit Density Approximation. We then discuss the main tools for performing ICA: the mutual information criterion, the nongausianity indexes, the exploitation of time correlation and nonstationarity. We provide in some details the algorithms to minimize the mutual information and for joint diagonalization. Finally some simulations are given illustrating the method.