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Blind Source Separation: Finding Needles in Haystacks

Blind Source Separation: Finding Needles in Haystacks. Scott C. Douglas Department of Electrical Engineering Southern Methodist University douglas@lyle.smu.edu. Signal Mixtures are Everywhere. Cell Phones Radio Astronomy Brain Activity Speech/Music. How do we make sense of it all?.

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Blind Source Separation: Finding Needles in Haystacks

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  1. Blind Source Separation: Finding Needles in Haystacks Scott C. Douglas Department of Electrical Engineering Southern Methodist University douglas@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)= ai1s1(k)+ai2s2(k)+ … +aimsm(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)= bi1x1(k) +bi2x2(k) + … +bim xm(k) up to permutation and scaling factors (the matrixB“is like”the inverse ofmatrixA) Problem:How do you find thedemixing bij’s when you don’t know themixing aij’sor 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-independent 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. In physics, entropy increases (less order) • In biology, entropy decreases (more order) 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. Separation System B(z) is a multichannel filter 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 ( > 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 allthe 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. 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. Speech Enhancement via Iterative Multichannel Filtering

  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 (RT=600ms) • 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. 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: Audio Examples

  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 arm’s 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. s(k) x(k) y(k) Complex Blind Source Separation 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 Bis complex-valued as well. • It appears that there is little difference from the real-valued case…

  34. Circular Circular Non-Circular 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 aren’t mistakes!

  37. Performance Comparisons

  38. Original Sources Sensor Signals CFPA1 Outputs 16-elem ULA, /4Spacing 3000 Snapshots SINRs/elem: -17,-12,-5,-12,-12 (dB) . DOAs(o): -45,20,-15,49,35 Output SINRs (dB): 7,24,18,15,23 Complexity: ~3500 FLOPS per output sample 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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