Model-based source separation

From: Tomi Kinnunen (tkinnu_at_cs.joensuu.fi)
Date: 11/18/04 

Date: Thu, 18 Nov 2004 04:31:16 +0000 (UTC)

Hi there,

Apologies for cross-posting; I'm not sure in what newsgroup I should
post my question.

There seems to be a lot of literature about signal separation algorithms that
are based on statistical independence assumption of the signals (ICA).
Often it is also assumed that there are many channels available (e.g.
several microphones). However, my interest is in the single-channel case.

My intuition (wrong ?????) says that it would be possible to do
separation/source detection from a single channel, having the following:

        1) p.d.f. estimates for each source, trained
           on the "clean" data of that source :
                
                p(x|Source1), ... , p(x|SourceN)

        2) Assumption of the independence of the sources

Let me try to be a bit more formal. Suppose we observe a feature vector
x that is known to be mixed from several sources :

        x = a_1*x_1 + a_2*x_2 + ... + a_N*x_N

, where a_i are scalars and x_i vectors, assumed to be drawn from
the given distributions. The observed vectors vary with time [I dropped
time indices for clarity].

My question is :

     Is there a known algorithm for solving a_i and x_i in this case ?

I've tried Googling something like "model-based source separation", but
obviously my search string is wrong. Please guide me to the right
direction. Any help is appreciated.

Apologies for possible layman terminology, I'm new to
source separation :-)

Sincerily yours,

Tomi K.

---------------------
Tomi Kinnunen
Researcher, PhLic
University of Joensuu
Finland
---------------------