Re: Model-based source separation

From: shankar (v.shankar_at_gmx.de)
Date: 11/18/04 

Date: 18 Nov 2004 15:05:03 -0800

Single-channel source separation is achieved by first representing the
signal in the time-frequency(TF) domain. Transforms like STFT,
Wavelets, ERB etc. can be used. ICA is then performed on the TF
matrix.

Ref:
1."Redundancy Reduction for Computational Audition, a Unifying
Approach", PhD thesis, Paris Smaragdis, Massachusetts Institute of
Technology, Media Laboratory, May 2001.
http://web.media.mit.edu/~paris/phd/

2. "Separation of Mixed Audio Sources by Independent Subspace
Analysis", Michael A. Casey, September 2001.
http://www.merl.com/reports/docs/TR2001-31.pdf

3. "Auditory Group Theory with Applications to Statistical Basis
Methods for Structured Audio", PhD thesis, Michael Anthony Casey,
Massachusetts Institute of Technology Media Laboratory, February 1998.
http://xenia.media.mit.edu/~mkc/thesis/

Hope this helps,
Shankar.

Tomi Kinnunen <tkinnu@cs.joensuu.fi> wrote in message news:<cnh8ik$o21$1@news.cs.joensuu.fi>...
> 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
> ---------------------

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