Frequency-domain Criterion for Speech Distortion Weighted Multi-Channel Wiener Filtering

1. Frequency-domain Criterion for Speech Distortion Weighted Multi-Channel Wiener Filtering Simon Doclo1, Ann Spriet1,2, Marc Moonen1, Jan Wouters2 1Dept. of Electrical Engineering (ESAT-SCD), KU Leuven, Belgium 2Laboratory for Exp. ORL, KU Leuven, Belgium HSCMA-2005, 17.03.2005

2. Overview • Adaptive beamforming: GSC • Not robust against signal model errors • Spatially-preprocessed SDW-MWF: • Increase robustness of adaptive stage by taking speech distortion into account • Implementation: stochastic gradient algorithms • Frequency-domain criterion • Experimental validation in hearing instruments • Audio demonstration • Conclusions

3. hearing aids and cochlear implants Hearing instruments • Hearing problems effect more than 10% of population • Digital hearing instruments allow for advanced signal processing, resulting in improved speech understanding • Major problem: (directional) hearing in background noise • reduction of noise wrt useful speech signal • multiple microphones + DSP in BTE • current systems: simple fixed and adaptive beamforming • robustness important due to small inter-microphone distance • Introduction • Adaptive beamforming • Experimental validation • Audio demo • Conclusions design of robust multi-microphone noise reduction scheme

4. Spatial pre-processor (Fixed beamforming) Adaptive stage (Adaptive Noise Canceller) 0° 0° speech reference + speech + noise - speech + noise - distorted speech + noise noise references 0° G Filter w1 noise + speech leakage Filter w2 Avoids speech distortion Minimises output noise power Relies on assumptions known mic characteristics, known speaker position, no reverberation Speech distortion ! Violated in practice GSC = Adaptive MVDR-beamformer • Introduction • Adaptive beamforming -GSC -SP-SDW-MWF -Implementation • Experimental validation • Audio demo • Conclusions

5. Speech component in output signal gets distorted Robustness against model errors • Spatial pre-processor and adaptive stage rely on assumptions that are generally not satisfied in practice: • Distortion of speech component in speech reference • Leakage of speech into noise references, i.e. • Introduction • Adaptive beamforming -GSC -SP-SDW-MWF -Implementation • Experimental validation • Audio demo • Conclusions • Design of robust noise reduction algorithm: • Reduce speech leakage contributions in noise references: • Robust fixed spatial filter[Nordebo 94, Doclo 03] • Adaptive blocking matrix[Van Compernolle 90, Hoshuyama 99, Herbordt 01] • Estimate relative acoustic transfer functions[Gannot 01] • Reduce effect of present speech leakage: • Only update adaptive filter during low-SNR periods/frequencies • Quadratic inequality constraint, leaky LMS[Cox 87, Claesson 92, Tian 01] • Take speech distortion explicitly into account, SDW-MWF[Spriet 04]

6. Quadratic inequality constraint (QIC-GSC): = conservative approach, constraint  f(amount of leakage) • Take speech distortion into account in optimisation criterion(SDW-MWF) • 1/ trades off noise reduction and speech distortion (1/ = 0  GSC, 1/ = 1  MMSE estimate) • Regularisation term ~ amount of speech leakage noise reduction speech distortion Limit speech distortion, while not affecting noise reduction performance in case of no model errors QIC Design of robust adaptive stage • Distorted speech in output signal: • Robustness: limit by controlling adaptive filter • Introduction • Adaptive beamforming -GSC -SP-SDW-MWF -Implementation • Experimental validation • Audio demo • Conclusions

7. regularisation term Classical GSC Implementation • Algorithms: • Recursive matrix-based (GSVD, QRD) – too expensive • Stochastic gradient algorithms (time vs. frequency domain) • Introduction • Adaptive beamforming -GSC -SP-SDW-MWF -Implementation • Experimental validation • Audio demo • Conclusions • Stochastic gradient algorithm (time-domain): • Cost function results in LMS-based updating formula • Practical computation of regularisation term using data buffers • Reduce complexity by frequency-domain implementation [Spriet 04]  Still large memory requirement due to data buffers • Memory reduction by approximating FD regularisation term [Doclo 04]

8. Recursive algorithm (details cf. book “Speech Enhancement”) Frequency-domain criterion (1) • Extension of block-based frequency-domain criterion for multi-channel AEC [Benesty 01, Buchner 03] • Set derivative wrt time-domain filter coefficients w to zero  normal equations in FD • Introduction • Adaptive beamforming -GSC -SP-SDW-MWF -Implementation • Experimental validation • Audio demo • Conclusions

9. Approximations for reducing the computational complexity: • Approximate and by block-diagonal(or diagonal) correlation matrices : • (block-)diagonal matrices can be easily inverted • Ensure that is positive-definite: eigenvalues of (block-)diagonal matrix can be easily computed • Constrained vs. unconstrained update : • corresponds to setting derivate wrt frequency-domain filter coefficients to zero Frequency-domain criterion (2) • Practical calculation of regularisation term averaging • Introduction • Adaptive beamforming -GSC -SP-SDW-MWF -Implementation • Experimental validation • Audio demo • Conclusions

10. mic 1 mic 2 mic 3 Noise 1 Noise 3 Noise 3 Noise 4 Noise 5 Experimental results Configuration • 3-mic BTE on dummy head (d = 1cm, 1.5cm) • Speech source in front of dummy head (0) • 5 speech-like noise sources: 75,120,180,240,285 • Gain mismatch = 4dB at 2nd microphone • Introduction • Adaptive beamforming • Experimental validation -Performance -Complexity • Audio demo • Conclusions Reverberation time= 500 msec H.A.

11. speech noise f Importance of i-th band for speech intelligibility - [dB] • Speech distortion input speech [dB] output speech f - [dB] Performance measures • Improvement in speech intelligibility • Introduction • Adaptive beamforming • Experimental validation -Performance -Complexity • Audio demo • Conclusions [dB]

12. GSC GSC Experimental validation (1) • SDR-GSC (unconstrained update) • Results after convergence (L=32, =0.5, =0.995, BD/D stepsize) • GSC (1/ = 0) : degraded performance if significant leakage • 1/ > 0 increases robustness (speech distortion  noise reduction) • Introduction • Adaptive beamforming • Experimental validation -Performance -Complexity • Audio demo • Conclusions

13. Experimental validation (2) • Convergence behaviour: • Convergence speed: block-diagonal step size > diagonal step size • large   fast convergence • large   slow convergence, better performance upon convergence • Introduction • Adaptive beamforming • Experimental validation -Performance -Complexity • Audio demo • Conclusions

14. Complexity and memory comparable to QIC-GSC Complexity + memory • Parameters: M = 3(mics), N = 2 (a), N = 3 (b), L= 32, fs = 16kHz, Ly = 10000 • Computational complexity: • Memory requirement: • Introduction • Adaptive beamforming • Experimental validation -Performance -Complexity • Audio demo • Conclusions

15. Audio demonstration • Introduction • Adaptive beamforming • Experimental validation • Audio demo • Conclusions (L=32, =10, =0.99875, block-diagonal stepsize, unconstrained update)

16. Conclusions • Spatially pre-processed SDW-MWF: • Take speech distortion explicitly into account  improve robustnessof adaptive stage • Encompasses GSC and MWF as special cases • Implementation: • Stochastic gradient algorithms in time- and frequency-domain • Frequency-domain criterion: block-based processing  natural derivation of different adaptive algorithms • Block-diagonal vs. diagonal, constrained vs. unconstrained • Comparable implementation cost as QIC-GSC • Experimental results: • SP-SDW-MWF achieves better noise reduction than QIC-GSC, for a given maximum speech distortion level • Faster convergence speed for block-diagonal step size matrix • Introduction • Adaptive beamforming • Experimental validation • Audio demo • Conclusions