Blind Source Separation: Finding Needles in Haystacks

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Blind Source Separation Finding Needles in
Haystacks
Scott C. Douglas Department of Electrical
Engineering Southern Methodist University douglas_at_
lyle.smu.edu
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Signal Mixtures are Everywhere

• Cell Phones
• Radio Astronomy
• Brain Activity
• Speech/Music

How do we make sense of it all?
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Example Speech Enhancement
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Example Wireless Signal Separation
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Example Wireless Signal Separation
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Example Wireless Signal Separation
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Example Wireless Signal Separation
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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

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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

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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?

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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.

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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.

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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.

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Convolutive Blind Source Separation

• Mixing system is dispersive

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Goal of Convolutive BSS

• Key idea For convolutive BSS, sources are
  arbitrarily filtered and arbitrarily shuffled

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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

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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

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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

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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

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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.

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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.

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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.

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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.
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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

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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
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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.

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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

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Performance Evaluations
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• 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)

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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

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Effect of Noise Segment Length on Overall
Performance
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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.

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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.

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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

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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.

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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.

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Complex Fixed Point Algorithm Douglas 2007

• NOTE The MATLAB code involves both transposes
  and Hermitian transposes and no, those arent
  mistakes!

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Performance Comparisons
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Complex BSS Example
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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.

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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