Design of a robust multi- Design of a robust multi- microphone noise reduction microphone noise reduction algorithm for hearing instruments algorithm for hearing instruments

(1)

Design of a robust multi- Design of a robust multi-

microphone noise reduction microphone noise reduction

algorithm for hearing instruments algorithm for hearing instruments

Simon Doclo

¹

, Ann Spriet

^1,2

, Marc Moonen

¹

, Jan Wouters

²

1

Dept. of Electrical Engineering (ESAT-SCD), KU Leuven, Belgium

2

Laboratory for Exp. ORL, KU Leuven, Belgium

MTNS-2004, 08.07.2004

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Overview Overview

• 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

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3

Problem statement 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

o reduction of noise wrt useful speech signal o multiple microphones + DSP

o 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

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State-of-the-art noise reduction State-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 different acoustic 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

Adaptive stage

Conclusions

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5

Adaptive beamforming: GSC Adaptive 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[k u

]

1[k u

]

1[k u_N_ Fixed

beamformer A(z) Speech

reference ]

0[k y

Blocking matrix

B(z) Noise

references ]

1[k y

]

2[k y

]

1[k y_N

Adaptive Noise Canceller

 

] [k z

]

1[k w

]

2[k w

]

1[k w_N_ (adaptation during noise)

]

0

[ k y

 

noise speech

] [ ]

[ ]

[ k x k v k y

_i



_i



_i

 



0 ²



]

[

[ ] [ ] [ ]

min E v k

^T

k k

k

w v

w

  

Introduction

Adaptive stage

Conclusions

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Robustness against model errors 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

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

[ k x 0 x [k ] 

Speech component in output signal gets distorted ]

[ ] [ ]

[ ]

[ k x

₀

k k k

z

_x

    w

^T

x

Limit distortion both in and x

₀

[ k ] w

^T

[ k ] x [ k ]

Introduction

Adaptive stage

Conclusions

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7

• 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-processor Robust spatial pre-processor

1 0

1

0

, , ) ( ) ( )

(

0 1





 





_N _N _N

A A

mean

J A A f A f A dA dA

J

N



Incorporate specific (random) deviations in design







 



  





_position

/ cos phase

) , ( gain

) , ( )

,

(

_n ^j ^j ^f ^c

n

a e

ⁿ

e

ⁿ ^s

A      

^ ^ ^ ^



^ ^ ^

Measurement or calibration procedure

Introduction

Adaptive stage

Conclusions

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Simulations Simulations

• N=3, positions: [-0.01 0 0.015] m, L=20, f

s

=8 kHz

• Passband = 0

^o

-60

^o

, 300-4000 Hz (endfire) Stopband = 80

^o

-180

^o

, 300-4000 Hz

• Robust design - average performance:

Uniform pdf = gain (0.85-1.15) and phase (-5

^o

-10

^o

)

• Deviation = [0.9 1.1 1.05] and [5

^o

-2

^o

5

^o

]

• Non-linear design procedure (only amplitude, no phase)

Introduction

Adaptive stage

Conclusions

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9

Non-robust design Robust design

No deviationsDeviations (gain/phase)

Simulations Simulations

Angle

(deg) Frequency

(Hz)

dB

Angle

(deg) Frequency

(Hz)

dB

Angle

(deg) Frequency

(Hz)

dB

Angle

(deg) Frequency

(Hz)

dB

Introduction

Adaptive stage

Conclusions

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Design of robust adaptive stage Design 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

] [ ] [ ]

[ ]

[ k x

₀

k k k

z

_x

    w

^T

x ]

[ ] [ k k

T

x

w w [k ]

 ] 

[k w

 



⁰ ²

  ^ ^

²



]

[

1 [ ] [ ]

] [ ] [ ]

[

min E v k

^T

k k E

^T

k k

k

w v w x

w

^ ^ ^ ^ 

noise reduction speech distortion

Limit speech distortion, while not affecting noise reduction performance in case of no model errors  QIC

Introduction

Adaptive stage -SP SDW MWF -Implementation -Experimental

validation

Conclusions

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12

Spatially-preprocessed SDW-MWF Spatially-preprocessed SDW-MWF

]

0[k w

Spatial preprocessing

]

0[k u

]

1[k u

]

1[k u_N

Fixed beamformer

A(z) Speech

reference ]

0[k y

Blocking matrix

B(z) Noise

references ]

1[k y

]

2[k y

]

1[k y_N

Multi-channel Wiener Filter (SDW-MWF)

 

] [k z

]

1[k w

]

2[k w

]

1[k w_N_

• 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

[ k w

]

0

[ k w

Introduction

validation

Conclusions

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Low-cost implementation Low-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/, w

0

)

• 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

 



0 ²

 1  ^ [ ] [ ] ^

²



] [ ] [ ]

[ )

( E v k k k E k k

J w w

^T

v w

^T

x

 









 

 ^[ ^] ^[ ^] ^[ ^] ^[ ^] 

] [ ]

1 [ k w k v k v

₀

k v

^T

k w k w       

regularisation term

] [ ] [ ] 1 [

k k

k x

^T

w

 x



Classical GSC

Introduction

validation

Conclusions

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15

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,285

o Microphone gain mismatch at 2

^nd

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

i

I SNR

i

SNR

1 intellig





i I

i

I SD

i

SD

1 intellig





 

c i

f

f x

i

f

df f

i

G

c i c

, 6 / 1 6

/ 1 2

2 10

2 2

) ( log

10 SD

6 , / 1



 

^

^G

^x

⁽ ^f ⁾ ^ _E ^E _ ^ _X ^Z

^x²²

⁽ ₍ ^f _f ⁾ ₎ ^ _

(Power Transfer Function for speech component)

Introduction

validation

Conclusions

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Experimental validation (2) Experimental validation (2)

• SDR-GSC:

o GSC (1/ = 0) : degraded performance if significant leakage

o 1/ > 0 increases robustness (speech distortion  noise reduction)

• SP-SDW-MWF:

o No mismatch: same , larger due to post-filter o Performance is not degraded by mismatch

0 w

₀



0 w

₀



intellig

 SNR SD

_intellig

Introduction

validation

Conclusions

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18

Audio demonstration Audio demonstration

Algorithm No deviation Deviation (4dB) Noisy microphone signal

Speech reference Noise reference Output GSC

Output SDR-GSC

Output SP-SDW-MWF

Introduction

validation

Conclusions

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Conclusions Conclusions

• 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

Adaptive stage

Conclusions