Blind signal separation

Blind signal separation, a.k.a. blind source separation, is the separation a set of independant signals from a set of mixed signals, with the aid of little or no information about the nature of the signals.

Blind signal separation riles on the two assumptions:

• The (independant) signals are statistically independant. This is reasonable enough, for if they were not statistically independant, they wouldn't be independant signals.
• The (independant) signals are not gaussian white noise. This is in any case a neccessary assumption. How can you tell white noise apart from white noise? It's the same: meaningless; random. However, the word signal implies that there is something about the signal which allows it to be distinguished; that there is something to be described by or about the signal, and thus that there is something regular about the signal; i.e. that there is regularity in the signal. Such regularity, being perhaps, a fact of "coming from" a given source, and that source having unique characterstics, thus giving the signal unique characteristics; regularities. These regularities make the signal non-gaussian, i.e., not completely irregular.

Blind signal separation thus separates a set of signals into a set of signals, such that the regularity of each resulting signal is maximized, and the regurality between the signals is minimized (statistical independance is maximized).

Because these temporal redundancies (statistical regularites in the time domain) are "clumped" in this way into the resulting signals, the resulting signals can be more effectively deconvolved than the original signals.

There are different methods of blind signal separation:

• Principal components analysis
• Singular value decomposition
• Independent components analysis

See also: blind deconvolution, Infomax principle, adaptive filtering