Independant Component Analysis

The problem of Blind Sources Separation (BSS)

In many real-life cases, you get sensors outputs, but you cannot measure directly the source signals of interest; you can only measure mixes of several sources.  Starting from these mixes, the aim of BSS consist in identifying the source signals.  ICA reaches this goal by assuming that the mixing process is linear and instantanuous.  Calling S the source signals, X the mixed signals, the problem can be written as follows: X = A*S, where A is an unknown mixing matrix.  Supposing that A is square (there as many sensors as sources) and non singular, a matrix W can be found such that Y = W*X and W = P*L*inv(A), where P is a permutation matrix and L a diagonal scaling matrix.  In other words, ICA can retrieve the source signals, except for one permutation and one power factor.  

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