Simon Doclo 1 , Ann Spriet 1,2 , Marc Moonen 1 , Jan Wouters 2

1. Design and low-cost implementation of a robust multichannel noise reduction scheme for cochlear implants 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 SPS-2004, 15.04.2004

2. Overview • Problem statement: hearing in background noise • Adaptive beamforming: GSC • not robust against model errors • Design of robust noise reduction algorithm • robust fixed spatial pre-processor • robust adaptive stage • Experimental results • Low-cost implementation of adaptive stage • stochastic gradient algorithms • computational complexity + memory • Conclusions

3. hearing aids and cochlear implants Problem statement • 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 • current systems: simple fixed and adaptive beamforming • robustness important due to small inter-microphone distance • Introduction -Problem statement -State-of-the-art -GSC • Robust spatial pre-processor • Adaptive stage • Implementation • Conclusions design of robust multi-microphone noise reduction scheme

4. Sensitive to a-priori assumptions State-of-the-art noise reduction • Single-microphone techniques: • spectral subtraction, Kalman filter, subspace-based • only temporal and spectral information  limited performance • Multi-microphone techniques: • exploit spatial information • Fixed beamforming: fixed directivity pattern • Adaptive beamforming (e.g. GSC): adapt to differentacoustic environments  improved performance • Multi-channel Wiener filtering (MWF): MMSE estimate of speech component in microphones  improved robustness • Introduction -Problem statement -State-of-the-art -GSC • Robust spatial pre-processor • Adaptive stage • Implementation • Conclusions Robust scheme, encompassing both GSC and MWF

5. Adaptive Noise Canceller Spatial pre-processing (adaptation during noise) Speechreference Fixed beamformer  S A(z) Blocking matrix B(z) Noise references Adaptive beamforming: GSC • Fixed spatial pre-processor: • Fixed beamformer creates speech reference • Blocking matrix creates noise references • Adaptive noise canceller: • Standard GSC minimises output noise power • Introduction -Problem statement -State-of-the-art -GSC • Robust spatial pre-processor • Adaptive stage • Implementation • Conclusions

6. Limit distortion both in and Robustness against model errors • Spatial pre-processor and adaptive stage rely on assumptions (e.g. no microphone mismatch, no reverberation,…) • In practice, these assumptions are often not satisfied • Distortion of speech component in speech reference • Leakage of speech into noise references, i.e. • Design of robust noise reduction algorithm: • Design of robust spatial pre-processor (fixed beamformer), e.g. using statistical knowledge about microphone characteristics • Design of robust adaptive stage, e.g. by taking speech distortion explicitly into account in optimisation criterion • Introduction -Problem statement -State-of-the-art -GSC • Robust spatial pre-processor • Adaptive stage • Implementation • Conclusions Speech component in output signal gets distorted

7. Measurement or calibration procedure Incorporate specific (random) deviations in design Robust spatial pre-processor • Small deviations from assumed microphone characteristics (gain, phase, position)  large deviations from desired directivity pattern, especially for small-size microphone arrays • In practice, microphone characteristics are never exactly known • Consider all feasible microphone characteristics and optimise • average performance using probability as weight • requires statistical knowledge about probability density functions • cost function: least-squares, eigenfilter, non-linear • worst-case performance  minimax optimisation problem • Introduction • Robust spatial pre-processor • Adaptive stage • Implementation • Conclusions

8. Simulations • N=3, positions: [-0.01 0 0.015] m, L=20, fs=8 kHz • Passband = 0o-60o, 300-4000 Hz (endfire)Stopband = 80o-180o, 300-4000 Hz • Robust design - average performance:Uniform pdf = gain (0.85-1.15) and phase (-5o-10o) • Deviation = [0.9 1.1 1.05] and [5o -2o 5o] • Non-linear design procedure (only amplitude, no phase) • Introduction • Robust spatial pre-processor • Adaptive stage • Implementation • Conclusions

9. dB dB dB dB Angle (deg) Angle (deg) Angle (deg) Angle (deg) Frequency (Hz) Frequency (Hz) Frequency (Hz) Frequency (Hz) Simulations • Introduction • Robust spatial pre-processor • Adaptive stage • Implementation • Conclusions

10. noise reduction speech distortion Design of robust adaptive stage • Distorted speech in output signal: • Robustness: limit by controlling adaptive filter • 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 • Regularisation term ~ amount of speech leakage • Introduction • Robust spatial pre-processor • Adaptive stage -SP SDW MWF -Experimental validation • Implementation • Conclusions Limit speech distortion, while not affecting noise reduction performance in case of no model errors QIC

11. speech-and-noise periods noise-only periods Wiener solution • Optimisation criterion: • Problem: clean speech and hence speech correlation matrix are unknown! Approximation: • VAD (voice activity detection) mechanism required! • Introduction • Robust spatial pre-processor • Adaptive stage -SP SDW MWF -Experimental validation • Implementation • Conclusions

12. Multi-channel Wiener Filter (SDW-MWF) Spatial preprocessing Speechreference Fixed beamformer  S A(z) Blocking matrix B(z) Noise references Spatially-preprocessed SDW-MWF • SP-SDW-MWF encompasses both GSC and SDW-MWF: • No filter   speech distortion regularised GSC (SDR-GSC) • regularisation term added to GSC: the larger the speech leakage, the larger the regularisation • special case: 1/ = 0corresponds to traditional GSC • Filter  SDW-MWF on pre-processed microphone signals • in absence of model errors = cascade of GSC + single-channel postfilter • Model errors do not effect its performance! • Introduction • Robust spatial pre-processor • Adaptive stage -SP SDW MWF -Experimental validation • Implementation • Conclusions

13. Experimental validation (1) • Set-up: • 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 • Microphone gain mismatch at 2nd microphone • Performance measures: • Intelligibility-weighted signal-to-noise ratio • Ii = band importance of i th one-third octave band • SNRi= signal-to-noise ratio in i th one-third octave band • Intelligibility-weighted spectral distortion • SDi= average spectral distortion in i th one-third octave band • Introduction • Robust spatial pre-processor • Adaptive stage -SP SDW MWF -Experimental validation • Implementation • Conclusions (Power Transfer Function for speech component)

14. Experimental validation (2) • SDR-GSC: • GSC (1/ = 0) : degraded performance if significant leakage • 1/ > 0 increases robustness (speech distortion  noise reduction) • SP-SDW-MWF: • No mismatch: same as SDR-GSC, larger due to post-filter • Performance is not degraded by mismatch • Introduction • Robust spatial pre-processor • Adaptive stage -SP SDW MWF -Experimental validation • Implementation • Conclusions

15. QIC  f(amount of speech leakage)  less noise reduction than SDR-GSC for small mismatch SP-SDW-MWF achieves better noise reduction than QIC-GSC, for a given maximum speech distortion level Experimental validation (3) • GSC with QIC ( ) : QIC increases robustness GSC • For large mismatch: less noise reduction than SP-SDW-MWF • Introduction • Robust spatial pre-processor • Adaptive stage -SP SDW MWF -Experimental validation • Implementation • Conclusions

16. Audio demonstration • Introduction • Robust spatial pre-processor • Adaptive stage -SP SDW MWF -Experimental validation • Implementation • Conclusions

17. Low-cost implementation (1) • Algorithms (in decreasing order of complexity): • GSVD-based – chic et très cher • QRD-based, fast QRD-based – chic et moins cher • Stochastic gradient algorithms – chic et pas cher • Stochastic gradient algorithm (time-domain) : • Cost function results in LMS-based updating formula • Allows transition to classical LMS-based GSC by tuning some parameters (1/,w0) • Introduction • Robust spatial pre-processor • Adaptive stage • Implementation -Stochastic gradient -Complexity and memory • Conclusions Classical GSC regularisation term

18. Low-cost implementation (2) • Stochastic gradient algorithm (time-domain): • Regularisation term is unknown • Store samples in memory buffer during speech-and-noise periods and approximate regularisation term • Better estimate of regularisation term can be obtained by smoothing (low-pass filtering) • Stochastic gradient algorithm (frequency-domain): • Block-based implementation: fast convolution and fast correlation Complexity reduction Tuning of  and 1/ per frequency Still large memory requirement due to data buffers • Approximation of regularisation term in FD allows to replace data buffers by correlation matrices memory + computational complexity reduction (cf. poster) • Introduction • Robust spatial pre-processor • Adaptive stage • Implementation -Stochastic gradient -Complexity and memory • Conclusions Large buffer required

19. Complexity comparable to FD implementation of QIC-GSC Substantial memory reduction through FD-approximation Complexity + memory • Parameters: N = 3(mics), M = 2 (a), M = 3 (b), L= 32, fs = 16kHz, Ly = 10000 • Computational complexity: • Memory requirement: • Introduction • Robust spatial pre-processor • Adaptive stage • Implementation -Stochastic gradient -Complexity and memory • Conclusions

20. Spatially pre-processed SDW Multichannel Wiener Filter Conclusions • Design of robust multimicrophone noise reduction algorithm: • Design of robust fixed spatial preprocessor  need for statistical information about microphones • Design of robust adaptive stage  take speech distortion into account in cost function • SP-SDW-MWF encompasses GSC and MWF as special cases • Experimental results: • SP-SDW-MWF achieves better noise reduction than QIC-GSC, for a given maximum speech distortion level • Filter w0improves performance in presence of model errors • Implementation: stochastic gradient algorithms available at affordable complexity and memory • Introduction • Robust spatial pre-processor • Adaptive stage • Implementation • Conclusions