independent Component Analysis: algorithms and applications

Motivation

Imagine a room where two people are speaking at the same time and two microphones are used to record the speech signals. Denoting the speech signals by [math]\displaystyle{ s_1(t) \, }[/math] and [math]\displaystyle{ s_2(t)\, }[/math] and the recorded signals by [math]\displaystyle{ x_1(t) \, }[/math] and [math]\displaystyle{ x_2(t) \, }[/math], we have the linear equation [math]\displaystyle{ x = As \, }[/math], where [math]\displaystyle{ A \, }[/math] is a parameter matrix that depends on the distances of the microphones from the speakers. The interesting problem of estimating both [math]\displaystyle{ A\, }[/math] and [math]\displaystyle{ s\, }[/math] using only the recorded signals [math]\displaystyle{ x\, }[/math] is called the cocktail-party problem, which is the signature problem for ICA.