1. Simon Doclo1, Ann Spriet1,2, Marc Moonen1, Jan Wouters2
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,

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. Problem statement Hearing problems effect more than 10% of population
Introduction
-Problem statement
-State-of-the-art
-GSC
Robust spatial
pre-processor
Adaptive stage
Implementation
Conclusions
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
hearing aids and cochlear implants
design of robust multi-microphone noise reduction scheme

4. State-of-the-art noise reduction
Introduction
-Problem statement
-State-of-the-art
-GSC
Robust spatial
pre-processor
Adaptive stage
Implementation
Conclusions
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 different acoustic environments  improved performance
Multi-channel Wiener filtering (MWF): MMSE estimate of speech component in microphones  improved robustness
Sensitive to a-priori assumptions
Robust scheme, encompassing both GSC and MWF

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

6. Robustness against model errors
Introduction
-Problem statement
-State-of-the-art
-GSC
Robust spatial
pre-processor
Adaptive stage
Implementation
Conclusions
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
Speech component in output signal gets distorted
Limit distortion both in and

7. 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
Incorporate specific (random) deviations in design
Measurement or calibration procedure

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

9. Simulations Non-robust design Robust design No deviations
Deviations (gain/phase)
Introduction
Robust spatial
pre-processor
Adaptive stage
Implementation
Conclusions
Angle (deg)
Frequency (Hz) dB
Angle (deg)
Frequency (Hz) dB
Angle (deg)
Frequency (Hz) dB
Angle (deg)
Frequency (Hz) dB

10. Design of robust adaptive stage
Introduction
Robust spatial
pre-processor
Adaptive stage
-SP SDW MWF
-Experimental validation
Implementation
Conclusions
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
noise reduction
speech distortion
Limit speech distortion, while not affecting noise reduction performance in case of no model errors  QIC

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

12. Spatially-preprocessed SDW-MWF
Spatial preprocessing
Fixed beamformer
A(z)
Speech reference
Blocking matrix
B(z)
Noise references
Multi-channel Wiener Filter (SDW-MWF) S 
Introduction
Robust spatial
pre-processor
Adaptive stage
-SP SDW MWF
-Experimental validation
Implementation
Conclusions
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/ = 0 corresponds 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!

13. Experimental validation (1)
Introduction
Robust spatial
pre-processor
Adaptive stage
-SP SDW MWF
-Experimental validation
Implementation
Conclusions
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
(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. 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
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

16. Audio demonstration Algorithm No deviation Deviation (4dB)
Noisy microphone signal
Speech reference
Noise reference
Output GSC
Output SDR-GSC
Output SP-SDW-MWF
Introduction
Robust spatial
pre-processor
Adaptive stage
-SP SDW MWF
-Experimental validation
Implementation
Conclusions

17. Low-cost implementation (1)
Introduction
Robust spatial
pre-processor
Adaptive stage
Implementation
-Stochastic gradient
-Complexity and memory
Conclusions
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)
Classical GSC
regularisation term

18. Low-cost implementation (2)
Introduction
Robust spatial
pre-processor
Adaptive stage
Implementation
-Stochastic gradient
-Complexity and memory
Conclusions
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)
Large buffer required

19. Complexity + memory
Introduction
Robust spatial
pre-processor
Adaptive stage
Implementation
-Stochastic gradient
-Complexity and memory
Conclusions
Parameters: N = 3 (mics), M = 2 (a), M = 3 (b), L = 32, fs = 16kHz, Ly = 10000
Computational complexity:
Memory requirement:
Algorithm
Complexity (MAC)
MIPS
QIC-GSC
(3N-1)FFT + 16N - 9
2.16
SDW-MWF (buffer)
(3M+5)FFT + 30M + 10
3.22 (a), 4.27 (b)
SDW-MWF (matrix)
(3M+2)FFT + 10M2 + 15M + 4
2.71 (a), 4.31 (b)
Complexity comparable to FD implementation of QIC-GSC
Algorithm
Memory
kWords
QIC-GSC
4(N-1)L + 6L
0.45
SDW-MWF (buffer)
2MLy + 6LM + 7L
40.61 (a), (b)
SDW-MWF (matrix)
4LM2 + 6LM + 7L
1.12 (a), 1.95 (b)
Substantial memory reduction through FD-approximation

20. Conclusions
Introduction
Robust spatial
pre-processor
Adaptive stage
Implementation
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 w0 improves performance in presence of model errors
Implementation: stochastic gradient algorithms available at affordable complexity and memory
Spatially pre-processed SDW Multichannel Wiener Filter