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Title: Blind Source Separation: Finding Needles in Haystacks


1
Blind Source Separation Finding Needles in
Haystacks
Scott C. Douglas Department of Electrical
Engineering Southern Methodist University douglas_at_
lyle.smu.edu
2
Signal Mixtures are Everywhere
  • Cell Phones
  • Radio Astronomy
  • Brain Activity
  • Speech/Music

How do we make sense of it all?
3
Example Speech Enhancement
4
Example Wireless Signal Separation
5
Example Wireless Signal Separation
6
Example Wireless Signal Separation
7
Example Wireless Signal Separation
8
Outline of Talk
  • Blind Source Separation
  • General concepts and approaches
  • Convolutive Blind Source Separation
  • Application to multi-microphone speech recordings
  • Complex Blind Source Separation
  • What differentiates the complex-valued case
  • Conclusions

9
Blind Source Separation (BSS) -A Simple Math
Example
s(k)
x(k)
y(k)
A
B
  • Let s1(k), s2(k),, sm(k) be signals of interest
  • Measurements For 1 i m,
  • xi(k) ai1 s1(k) ai2 s2(k) aim sm(k)
  • Sensor noise is neglected
  • Dispersion (echo/reverberation) is absent

10
Blind Source Separation Example (continued)
s(k)
x(k)
y(k)
A
B
  • Can Show The si(k)s can be recovered as
  • yi(k) bi1 x1(k) bi2 x2(k) bim xm(k)
  • up to permutation and scaling factors (the
  • matrix B is like the inverse of matrix A)
  • Problem How do you find the demixing bijs
  • when you dont know the mixing aijs or sj(k)s?

11
Why Blind Source Separation?(Why not Traditional
Beamforming?)
  • BSS requires no knowledge of sensor geometry.
    The system can be uncalibrated, with unmatched
    sensors.
  • BSS does not need knowledge of source positions
    relative to the sensor array.
  • BSS requires little to no knowledge of signal
    types - can push decisions/ detections to the end
    of the processing chain.

12
What Properties Are Necessary for BSS to Work?
  • Separation can be achieved when
  • ( sensors) ( of sources)
  • The talker signals sj(t) are statistically-indep
    endent of each other and
  • are non-Gaussian in amplitude
  • OR
  • have spectra that differ from each other
  • OR
  • are non-stationary
  • Statistical independence is the critical
    assumption.

13
Entropy is the Key to Source Separation
  • Entropy A measure of regularity
  • In BSS, separated signals are demixed and, have
    more order as a group.
  • First used in 1996 for speech separation.

14
Convolutive Blind Source Separation
  • Mixing system is dispersive

15
Goal of Convolutive BSS
  • Key idea For convolutive BSS, sources are
    arbitrarily filtered and arbitrarily shuffled

16
Non-Gaussian-Based Blind Source Separation
  • Basic Goal Make the output signals look
    non-Gaussian, because mixtures look more
    Gaussian (from the Central Limit Theorem)
  • Criteria Based On This Goal
  • Density Modeling
  • Contrast Functions
  • Property Restoral e.g. (Non-)Constant Modulus
    Algorithm
  • Implications
  • Separating capability of the criteria will be
    similar
  • Implementation details (e.g. optimization
    strategy) will yield performance differences

17
BSS for Convolutive Mixtures
  • Idea Translate separation task into frequency
    domain and apply multiple independent
    instantaneous BSS procedures
  • Does not work due to permutation problems
  • A Better Idea Reformulate separation tasks in
    the context of multichannel filtering
  • Separation criterion stays in the time domain
    no implied permutation problem
  • Can still employ fast convolution methods for
    efficient implementation

18
Natural Gradient Convolutive BSS Alg.
Amari/Douglas/Cichocki/Yang 1997
  • where f(y) is a simple vector-valued
    nonlinearity.
  • Criterion Density-based (Maximum Likelihood)
  • Complexity about four multiply/adds per tap

19
Blind Source Separation Toolbox
  • A MATLAB toolbox of robust source separation
    algorithms for noisy convolutive mixtures
    (developed under govt. contract)
  • Allows us to evaluate relationships and tradeoffs
    between different approaches easily and rapidly
  • Used to determine when a particular algorithm or
    approach is appropriate for a particular
    (acoustic) measurement scenario

20
Speech Enhancement Methods
  • Classic (frequency selective) linear filtering
  • Only useful for the simplest of situations
  • Single-microphone spectral subtraction
  • Only useful if the signal is reasonably
    well-separated to begin with ( gt 5dB SINR )
  • Tends to introduce musical artifacts
  • Research Focus How to leverage multiple
    microphones to achieve robust signal enhancement
    with minimal knowledge.

21
Novel Techniques for Speech Enhancement
  • Blind Source Separation Find all the talker
    signals in the room - loud and soft, high and
    low-pitched, near and far away without
    knowledge of any of these characteristics.
  • Multi-Microphone Signal Enhancement Using only
    the knowledge of target present or target
    absent labels on the data, pull out the target
    signal from the noisy background.

22
SMU Multimedia Systems LabAcoustic Facility
  • Room (Nominal Configuration)
  • Acoustically-treated
  • RT 300 ms
  • Non-parallel walls to prevent flutter echo
  • Sources
  • Loudspeakers playing Recordings as well as live
    talkers.
  • Distance to mics 50 cm
  • Angles -30o, 0o, 27.5o
  • Sensors
  • Omnidirectional Micro- phones (AT803b)
  • Linear array (4cm spacing)
  • Data collection and processing entirely within
    MATLAB.
  • Allows for careful characterization, fast
    evaluation, and experimentation with artificial
    and human talkers.

23
Blind Source Separation Example
Talker 1 (MG)
Convolutive Mixing (Room)
Separation System (Code)
Talker 2 (SCD)
Performance improvement Between 10 dB and 15 dB
for equal-level mixtures, and even higher for
unequal-level ones.
24
Unequal Power Scenario Results
  • Time-domain CBSS methods provide the greatest SIR
    improvements for weak sources no significant
    improvement in SIR if the initial SIR is already
    large

25
Multi-Microphone Speech Enhancement
Noise Source
Contains most speech
y1
z1
y2
z2
Linear Processing
Noise Source
y3
z3
yn
zn
Contains most noise
Speech Source
Adaptive Algorithm
26
Speech Enhancement via Iterative Multichannel
Filtering
  • System output at time k a linear adaptive filter
  • is a sequence of (n x n) matrices
    at iteration k.
  • Goal Adapt , over
    time such that the multichannel output
    contains signals with maximum speech energy in
    the first output.

27
Multichannel Speech Enhancement Algorithm
  • A novel technique for enhancing target speech in
    noise using two or more microphones via joint
    decorrelation
  • Requires rough target identifier (i.e. when
    talker speech is present)
  • Is adaptive to changing noise characteristics
  • Knowledge of source locations, microphone
    positions, other characteristics not needed.
  • Details in Gupta and Douglas, IEEE Trans. Audio,
    Speech, Lang. Proc., May 2009
  • Patent pending

28
Performance Evaluations
7
6
8
8
7
6
  • Room
  • Acoustically-treated, RT 300 ms
  • Non-parallel walls to prevent flutter echo
  • Sources
  • Loudspeakers playing BBC Recordings (Fs 8kHz),
    1 male/1-2 noise sources
  • Distance to mics 1.3 m
  • Angles -30o, 0o, 27.5o
  • Sensors
  • Linear array adjustable (4cm spacing)
  • Room
  • Ordinary conference room (RT600ms)
  • Sources
  • Loudspeakers playing BBC Recordings (Fs 8kHz),
    1 male/1-2 noise sources
  • Angles -15o, 15o, 30o
  • Sensors
  • Omnidirectional Microphones (AT803b)
  • Linear array adjustable (4cm nominal spacing)

28
29
Audio Examples
  • Acoustic Lab Initial SIR -10dB, 3-Mic System
  • Before After
  • Acoustic Lab Initial SIR 0dB, 2-Mic
    SystemBefore After
  • Conference Room Initial SIR -10dB, 3-Mic
    System
  • Before After
  • Conference Room Initial SIR 5dB, 2-Mic System
  • Before After

30
Effect of Noise Segment Length on Overall
Performance
31
Diffuse Noise Source Example
  • Noise Source SMU Campus-Wide Air Handling
    System
  • Data was recorded using a simple two-channel
    portable M-Audio recorder (16-bit, 48kHz) with it
    associated T-shaped omnidirectional stereo
    array at arms length, then downsampled to 8kHz.

31
32
Air Handler Data Processing
  • Step 1 Spatio-Temporal GEVD Processing on a
    frame-by-frame basis with L 256, where Rv(k)
    Ry(k-1) that is, data was whitened to the
    previous frame.
  • Step 2 Least-squares multichannel linear
    prediction was used to remove tones.
  • Step 3 Log-STSA spectral subtraction was applied
    to the first output channel.

32
33
Complex Blind Source Separation
s(k)
x(k)
y(k)
A
B
  • Signal Model
  • x(k) A s(k)
  • Both the si(k)s in s(k) and the elements of
    A are complex-valued.
  • Separating matrix B is complex-valued as well.
  • It appears that there is little difference from
    the real-valued case

34
Complex Circular vs. Complex Non-Circular Sources
  • (Second-Order) Circular Source The energies of
    the real and imaginary parts of si(k) are the
    same.
  • (Second-Order) Non-Circular Source The energies
    of the real and imaginary parts of si(k) are not
    the same.

35
Why Complex Circularity Matters in Blind Source
Separation
  • Fact 1 It is possible to separate non-circular
    sources by decorrelation alone if their
    non-circularities differ Eriksson and Koivunen,
    IEEE Trans. IT, 2006
  • Fact 2 The strong-uncorrelating transform is a
    unique linear transformation for identifying
    non-circular source subspaces using only
    covariance matrices.
  • Fact 3 Knowledge of source non-circularity is
    required to obtain the best performance of a
    complex BSS procedure.

36
Complex Fixed Point Algorithm Douglas 2007
  • NOTE The MATLAB code involves both transposes
    and Hermitian transposes and no, those arent
    mistakes!

37
Performance Comparisons
38
Complex BSS Example
39
Conclusions
  • Blind Source Separation provides unique
    capabilities for extracting useful signals from
    multiple sensor measurements corrupted by noise.
  • Little to no knowledge of the sensor array
    geometry, the source positions, or the source
    statistics or characteristics is required.
  • Algorithm design can be tricky.
  • Opportunities for applications in speech
    enhancement, wireless communications, other
    areas.

40
For Further Reading
  • My publications page at SMU
  • http//lyle.smu.edu/douglas/puball.html
  • It has available for download
  • 82 of my published journal papers
  • 75 of my published conference papers
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