Design of a robust multi-Design of a robust multi-
microphone noise reduction microphone noise reduction
algorithm for hearing instrumentsalgorithm for hearing instruments
Simon Doclo1, Ann Spriet1,2, Marc Moonen1, Jan Wouters2
1Dept. of Electrical Engineering (ESAT-SCD), KU Leuven, Belgium2Laboratory for Exp. ORL, KU Leuven, Belgium
MTNS-2004, 08.07.2004
22
OverviewOverview
• Problem statement: hearing in background noise
• Adaptive beamforming: GSC
o not robust against model errors
• Design of robust noise reduction algorithm
o robust fixed spatial pre-processor
o robust adaptive stage
• Low-cost implementation of adaptive stage
• Experimental results + demo
• Conclusions
33
Problem statementProblem 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 noiseo reduction of noise wrt useful speech signalo multiple microphones + DSPo current systems: simple fixed and adaptive
beamforming o robustness important due to small inter-microphone
distance
hearing aids and cochlear implants
design of robust multi-microphone noise reduction scheme
Introduction -Problem statement
-State-of-the-art -GSC Robust spatial pre-processor
Adaptive stage Conclusions
44
State-of-the-art noise reductionState-of-the-art noise reduction
• Single-microphone techniques:
o spectral subtraction, Kalman filter, subspace-based
o only temporal and spectral information limited performance
• Multi-microphone techniques:
o exploit spatial information
o Fixed beamforming: fixed directivity pattern
o Adaptive beamforming (e.g. GSC) : adapt to differentacoustic environments improved performance
o 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
Introduction -Problem statement
-State-of-the-art -GSC Robust spatial pre-processor
Adaptive stage Conclusions
55
Adaptive beamforming: GSCAdaptive beamforming: GSC
• Fixed spatial pre-processor:o Fixed beamformer creates speech reference o Blocking matrix creates noise references
• Adaptive noise canceller:o Standard GSC minimises output noise power
Spatial pre-processing][0 ku
][1 ku
][1 kuN
Fixed beamformer
A(z)
Speechreferenc
e ][0 ky
Blocking matrixB(z)
Noise references
][1 ky
][2 ky
][1 kyN
Adaptive Noise Canceller
][kz
][1 kw
][2 kw
][1 kwN
(adaptation during noise)
][0 ky
noisespeech
][][][ kvkxky iii
2
0][
][][][min kkkvE T
kvw
w
Introduction -Problem statement
-State-of-the-art -GSC Robust spatial pre-processor
Adaptive stage Conclusions
66
Robustness against model errorsRobustness 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
o Distortion of speech component in speech reference
o Leakage of speech into noise references, i.e.
• Design of robust noise reduction algorithm:
1. Design of robust spatial pre-processor (fixed beamformer)
2. Design of robust adaptive stage
][0 kx
0x ][k
Speech component in output signal gets distorted
][][][][ 0 kkkxkz Tx xw
Limit distortion both in and ][0 kx ][][ kkT xw
Introduction -Problem statement
-State-of-the-art -GSC Robust spatial pre-processor
Adaptive stage Conclusions
77
• 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
o average performance using probability as weight
– requires statistical knowledge about probability density functions
– cost function J : least-squares, eigenfilter, non-linear
o worst-case performance minimax optimisation problem
Robust spatial pre-processorRobust spatial pre-processor
101010 )()(),,(0 1
NNN
A A
mean dAdAAfAfAAJJN
Incorporate specific (random) deviations in design
position
/cos
phase
),(
gain
),(),( cfjjnn
snn eeaA
Measurement or calibration procedure
Introduction Robust spatial pre-processor
Adaptive stage Conclusions
88
SimulationsSimulations
• 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 Conclusions
99
Non-robust design Robust design
No d
evia
tions
Devia
tions (g
ain
/phase
)
SimulationsSimulations
Angle (deg)
Frequency (Hz)
dB
Angle (deg)
Frequency (Hz)
dB
Angle (deg)
Frequency (Hz)
dB
Angle (deg)
Frequency (Hz)
dB
Introduction Robust spatial pre-processor
Adaptive stage Conclusions
1010
Design of robust adaptive stageDesign of robust adaptive stage
• Distorted speech in output signal:
• Robustness: limit by controlling adaptive filter
o Quadratic inequality constraint (QIC-GSC):
= conservative approach, constraint f (amount of leakage)
o Take speech distortion into account in optimisation criterion(SDW-MWF)
– 1/ trades off noise reduction and speech distortion
– Regularisation term ~ amount of speech leakage
][][][][ 0 kkkxkz Tx xw
][][ kkT xw ][kw
][kw
22
0][
][][1
][][][min kkEkkkvE TT
kxwvw
w
noise reduction speech distortion
Limit speech distortion, while not affecting noise reduction performance in case of no model errors QIC
Introduction Robust spatial pre-processor
Adaptive stage -SP SDW MWF -Implementation -Experimental validation
Conclusions
1212
Spatially-preprocessed SDW-Spatially-preprocessed SDW-MWFMWF
][0 kw
Spatial preprocessing][0 ku
][1 ku
][1 kuN
Fixed beamformer
A(z)
Speechreferenc
e ][0 ky
Blocking matrixB(z)
Noise references
][1 ky
][2 ky
][1 kyN
Multi-channel Wiener Filter (SDW-MWF)
][kz
][1 kw
][2 kw
][1 kwN
• Generalised scheme, encompasses both GSC and SDW-MWF:
o No filter speech distortion regularised GSC (SDR-GSC)
– special case: 1/ = 0 corresponds to traditional GSC
o Filter SDW-MWF on pre-processed microphone signals
– Model errors do not effect its performance!
][0 kw
][0 kw
Introduction Robust spatial pre-processor
Adaptive stage -SP SDW MWF -Implementation -Experimental validation
Conclusions
1313
Low-cost implementationLow-cost implementation
• Stochastic gradient algorithm in time-domain:
o Cost function
results in LMS-based updating formula
o Approximation of regularisation term in TD using data buffers
o Allows transition to classical LMS-based GSC by tuning some parameters (1/, w0)
• Complexity reduction in frequency-domain:
o Block-based implementation: fast convolution and correlation
o Approximation of regularisation term in FD allows to replace data buffers by correlation matrices
22
0 ][][1
][][][)( kkEkkkvEJ TT xwvww
][][][][][]1[ 0 kkkvkkk T wvvww
regularisation term
][][][1
kkk T wxx
Classical GSC
Introduction Robust spatial pre-processor
Adaptive stage -SP SDW MWF -Implementation -Experimental validation
Conclusions
1515
Experimental validation (1)Experimental validation (1)
• Set-up:o 3-mic BTE on dummy head (d = 1cm, 1.5cm)
o Speech source in front of dummy head (0)o 5 speech-like noise sources: 75,120,180,240,285o Microphone gain mismatch at 2nd microphone
• Performance measures:o 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
o Intelligibility-weighted spectral distortion
– SDi = average spectral distortion in i th one-third octave band
2
i
I
iiI SNRSNR
1intellig
i
I
iiI SDSD
1intellig
ic
f
f x
i f
dffGic
ic
,6/16/1
2
2 10
22
)(log10SD
,6/1
,6/1
)(
)()(
2
2
fXE
fZEfG x
x
(Power Transfer Function for speech component)
Introduction Robust spatial pre-processor
Adaptive stage -SP SDW MWF -Implementation -Experimental validation
Conclusions
1616
Experimental validation (2)Experimental validation (2)• SDR-GSC:
o GSC (1/ = 0) : degraded performance if significant leakageo 1/ > 0 increases robustness (speech distortion noise
reduction)
• SP-SDW-MWF: o No mismatch: same , larger due to post-
filtero Performance is not degraded by mismatch
0w 0
0w 0
intelligSNR intelligSD
Introduction Robust spatial pre-processor
Adaptive stage -SP SDW MWF -Implementation -Experimental validation
Conclusions
1818
Audio demonstrationAudio demonstration
Algorithm No deviationDeviation (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 -Implementation -Experimental validation
Conclusions
1919
ConclusionsConclusions
• Design of robust multimicrophone noise reduction algorithm:
o Design of robust fixed spatial preprocessor
need for statistical information about microphones
o 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:
o SP-SDW-MWF achieves better noise reduction than QIC-GSC, for a given maximum speech distortion level
o 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
Introduction Robust spatial pre-processor
Adaptive stage Conclusions