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April - 2006 Signaler & SystemUppsala universitet
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Blind source separation
Introduction to blind source separation
Mathias Johansson
Lecture notes for the course “Adaptive signal processing”
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Blind source separation
Mixed signals are recorded
We want to demix the recordings and find s1(t) and s2(t)
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Blind source separation
Blind source separation• A number, M, of microphones record a mixture
of N source signals, for example: • several people talking in a room (the cocktail party
effect),• radio signals emitted from several mobile terminals and
received by others• electromagnetic signals from different brain regions
recorded by sensors on the head
• The job is to estimate the individual source signals, i.e. to demix the mixture, withoutknowledge about the actual sources.
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Blind source separation
Is this even possible??• Have you ever been to Orvars?
– Yes, it is possible (within reason)• But still, how to do it in a computer?
– Different approaches, but they all make use of assumptions or knowledge regarding the mixing process or the signals, e.g.
• ICA (Independent Component Analysis) only assumes that the sources are stat. independent
• DUET assumes that the signals are non-overlapping in the frequency domain, and a mixing model consisting of an anechoic environment.
April - 2006 Signaler & SystemUppsala universitet
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Blind source separation
Possible approaches• Beamforming:
– By delaying and attenuating the signals impinging on the recording array, a beam can be focused towards a certain direction
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Blind source separation
Beamforming example
Recording 1
Recording 2
Signal 1 Signal 2
Recording 2: Different delays due to different angles of arrival
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Blind source separation
Beamforming exampleA: Recording 1 delayed 500 samples
B: Recording 2
Beamforming: Average of A and B
Signal 1 is amplified whereas signal 2 is attenuated. The beamforming suppresses signals from certain angles.
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Blind source separation
Beamforming disadvantages• Can only distinguish signals that have well
separated angle-of-arrivals• Ad hoc technique relying on linear
processing, not optimal in general.• Need to estimate the delay (and
attenuation) of the desired source.
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Blind source separation
Independent Component Analysis• An approach that relies on assuming (almost)
only that the sources are statistically independent
• Assumes a linear instantaneous static mix:
• Using Bayes’ rule the most likely mixing matrix is computed
• Using the inverse of the estimated mixing matrix, the source signals are estimated
April - 2006 Signaler & SystemUppsala universitet
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Blind source separation
Independent Component Analysis• Works well for instantaneous static mixing • Generalizations to deal with echoes and
convolutive mixes exist, but exhibit poor performance
• We will not investigate ICA in the project
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Blind source separation
DUET• A relatively new approach that assumes
the following:– Signals are non-overlapping in the frequency
domain– Mixing model:
• Attenuation and delay (i.e. anaechoic mixtures)
• Can even handle cases when there are more signals than recordings
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Blind source separation
DUET algorithm outline1. Taking the DFT of a block of the recordings,
there is thus only one signal present in each frequency bin
2. Estimate the time delay and attenuation in each bin
3. Label the bins according to delay and attenuation
4. Each source signal is estimated by inverse-transforming the bins that have the same labels
April - 2006 Signaler & SystemUppsala universitet
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Blind source separation
DUET assumptionTime
FFT(x(1:N))
s1s1
s1
s1
s1s1
s1
s1
s2
s2
s2
s2s2
s2
s2
...
Freq
uenc
y
FFT of next block, etc.
At each time instant, each frequency bin contains only one signal, or no signal at all.
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Blind source separation
DUET algorithm• The mixing model can be described as
• N is the number of sourcesAttenuation Delay
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Blind source separation
DUET algorithm• Taking the DFT of both recorded signals,
we have
since only one signal, say the ith one, is non-zero at each frequency ω.– Recall that the Fourier transform of a delayed
signal is: DFT(s(t-d)) = exp(-jωd)S(ω)
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Blind source separation
DUET algorithm• We can then compute the amplitude and
delay of signal i from:
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Blind source separation
DUET algorithm• For each block of data and each frequency, we
get an amplitude and delay estimate.• We keep track of old estimates and form a two-
dimensional histogram of the amplitude-delay estimates
• There will be N clusters in the histogram, each one corresponding to a specific source
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Blind source separation
A histogram taken from [1]
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Blind source separation
DUET algorithm• We then label each frequency bin
according to the peak in the histogram that is closest to the current estimate
• To reconstruct a source signal icorresponding to a certain amplitude-delay peak in the histogram, just set all bins to zero that are not labelled as i.– Finally take the inverse Fourier transform!
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Blind source separation
Extensions• S. Rickard and co-workers have also
developed other versions of the algorithm– One is specially suited for real-time
implementations, check the project report from 2004 for more info.
– However, the current algorithm should work in real-time too.
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Blind source separation
Project focus 2006• The project set-up:
– 2 microphones, 2 acoustic source signals (speakers)
• Aim:– Based on results from 2004, implement a
working BSS system in real-time using Matlab• Compare the real-time algorithm used in
2004 with the histogram-based method
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Blind source separation
Project focus 2006• First, read the report from 2004 and the
background material [1]-[3] carefully• Begin with artificial mixes, i.e. generated
from Matlab• Then try anaechoic recordings (use the lab
on floor 2 at Magistern)
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Blind source separation
References[1] A. Jourjine, S. Rickard, Ö. Yilmaz, ”Blind separation of disjoint
orthogonal signals: demixing N sources from 2 mixtures”, ICASSP 2000.
[2] S. Rickard, R. Balan, J. Rosca, ”Real-time time-frequency based blind source separation”, ICA 2001.
[3] Ö. Yilmaz, S. Rickard, ”Blind separation of speech mixtures via time-frequency masking”, IEEE Trans. On Signal Processing, vol 52, no7, July 2004.