Blind Source Separation of Acoustic Signals Based on Multistage Independent Component Analysis

1
Blind Source Separation of Acoustic Signals Based
on Multistage Independent Component Analysis

• Hiroshi SARUWATARI,
• Tsuyoki NISHIKAWA, and Kiyohiro SHIKANO
• Graduate School of Information Science
• Nara Institute of Science and Technology

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Contents

• Background of blind source separation (BSS)
• Overview of Independent Component Analysis (ICA)
• Time-domain ICA (TDICA)
• Frequency-domain ICA (FDICA)
• Disadvantages of TDICA and FDICA
• Proposal of Multistage ICA
• Experimental results under real acoustic
  condition
• Conclusion

3
Background
Hands-free speech recognition system
Is it fine tomorrow?
Microphone
Target Speech
Speech recognition system
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Background (Contd)

• Goal
• Microphone array
• Receiver which consists of multiple elements
• To enhance target speech or reduce interference
• Problem of microphone array processing
• A priori information is required.
• Directions of arrival of the sound sources
• Breaks of target speech for filter adaptation

• Realization of high quality hands-free
• speech interface system

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Problem of Microphone Array

• Delay and Sumto produce narrow beam-pattern
• Adaptiveto update filters to reduce the noise

Target
High sidelobe gains noise.
?
It is necessary to observe only noise for filter
learning.
Set target direction.
?
Null
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Blind Source Separation (BSS)

• Approach taken to estimate source signals only
  from the observed mixed signals.
• Any information about source directions and
  acoustic conditions is not required.
• Independent component Analysis (ICA) is mainly
  used.
• Previous works on ICA
• J. Cardoso, 1989
• C. Jutten, 1990 (Higher-order
  decorrelation)
• P. Common, 1994 (define the term ICA)
• A. Bell et al., 1995 (infomax)

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ICA-Based BSS
No a priori information (unsupervised adaptive
filtering)
Good Morning!
Speaker1
Source1
Observed signal1
Microphone1
Microphone2
Observed signal2
Hello!
Source2
Speaker2
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BSS for Instantaneous mixture
Linearly Mixing Process
Mixing Matrix
Source
Observed
Separation Process
Unmixing Matrix
Separated
Optimize
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Various Criterion for ICA
Separated Signal

• Decorrelation
• To minimize correlation among signals
• in multiple time durations
• Nonlinear function 1
• To minimize higher-order correlation
• Nonlinear function 2
• To assume p.d.f of sources

Sigmoid function
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Cost Function for Nonlinear Function 2
Kullback-Leibler (KL) divergence between
and
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Derivation for Nonlinear Function 2
To update along the negative gradient of
Nonlinear Function 2 ? To be diagonalized
where
This can be approximated by Sigmoid Function in
speech signal.
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Why Instantaneous Mixture Model?

• ICA for Instantaneous Mixture model
• ? Mixing matrix is represented as real-valued.
• ? No assumption for time delay among
  microphones and room reflections.

Is it applicable to sound signals in real
acoustic environment?
NO!
It is a useful example to show how ICA can work,
but only mathematical Toy model.
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ICA for Convolutive Mixture Model (1)

• In application to microphone array,
• each received signal has a time delay which
  corresponds to the sound direction and position
  of each element.
• mixing matrix A is not simple scalar-valued
  coefficient,
• but is represented as convolution filter.

Mixing Process in Real Environment
Mixing Matrix (FIR-Filter)
Source
Observed
?We should use FIR filter for separation process.
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ICA for Convolutive Mixture Model (2)

• To simplify the convolutive mixture down to
• instantaneous mixtures by the frequency
  transform

Mixing Process in Frequency Domain
Complex-Valued Mixing Matrix
Source
observed
?We only solve the complex-valued instantaneous
mixture in each subband independently.
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Permutation Problem in FDICA
ICA is conducted in each subband
independently. Ordering and Scaling of outputs
are arbitrary in ICA.
Permutation and Gain Determinacy
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Solutions for Permutation Problem
To use correlation among outputs waveforms
(Murata et al. 1998) To use directivity pattern
of W (Kurita and Saruwatari, 2000) To use
correlation among unmixing matrices in
neighboring frequency bins (Parra et al, 2000,
Asano et al, 2001)
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Problem in ICA-Based BSS
Separation performance under reverberant
conditions significantly degrades.
Why?
Reverberation in typical room 2400-tap
FIR-filter in 8 kHz sampling ?The number of
parameters is too large.
It is necessary to achieve robust BSS method
against reverberation.
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Conventional Approaches

• Frequency-Domain ICA (FDICA)
• To estimate the separation coefficients every
  frequency bin in the frequency domain
• Time-Domain ICA (TDICA)
• To estimate the separation FIR filter in the time
  domain

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FDICA-Based BSS
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Performance of FDICA

• In conventional dereverberation processing,
  dereverberation performance is improved as the
  number of subbands (filter length) is enlarged.

ltSpeculationgt
In FDICA, as the number of subbands is enlarged,
is source-separation performance also improved?
To investigate the relation between the number of
subbands and source-separation performance
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Experimental Setup

• Interelement
• spacing is 4 cm.
• Reverberation time
• is 300 ms.

• Sound source
• 2-male and 2-female speech from ASJ corpus
• (12 combinations)
• Evaluation Noise Reduction Rate
• Output SNR dB Input SNR dB

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FDICA Algorithm

• Iterative learning algorithm (Amari, 1996)
• where

? Step size parameter
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Relation between Number of Subbands and
Separation Performance
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Narrow-Band Signals
Real part (1 kHz)
Signal1
Signal1
Signal2
Signal2
32-Subbands
2048-Subbands
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Relation between Number of Subbands and
Correlation
Higher correlation
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Trade-off Relation between Independence and
Robustness against Reverberation
High-Independence
Robust against Reverberation
Low- Independence
Poor against Reverberation
Noise Reduction Rate
Number of Subbands
Large
Small
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TDICA-Based BSS
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Performance of TDICA

• In conventional dereverberation processing,
  dereverberation performance is improved as the
  filter length is lengthened.

ltSpeculationgt
In TDICA, as the filter length is lengthened,
is source-separation performance also improved?
To investigate the relation between the filter
length and source-separation performance
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TDICA Algorithm

• Cost function

minimize
where
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TDICA Algorithm (Contd)

• Iterative equation of separation filter
• Natural gradient of Q(w(z))

where a is the step-size parameter
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Proposed Iterative Equation of TDICA

• Iterative equation of separation filter (TDICA1)

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Results of TDICA1 and TDICA2
TDICA 1 (only correlation of same time)
TDICA 2 (correlation of different time)
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Problems and Solution
FDICA
TDICA

• Advantages
• To simplify the convolutive mixture down to
  instantaneous mixtures
• Easy to converge the separation filter with high
  stability
• Disadvantages
• Independence assumption collapses in each
  narrow-band.
• Separation performance is saturated before
  reaching a sufficient performance.

• Advantages
• To treat the fullband speech signals where the
  independence assumption of sources usually holds
• High-convergence possibility near the optimal
  point
• Disadvantages
• Iterative rule for filter learning is
  complicated.
• Convergence degrades under reverberant conditions.

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Separation Procedure of MSICA
TDICA
FDICA
Mixing system

• Separated signals of FDICA are regarded
• as the input signals for TDICA.
• Residual cross-talk components of FDICA
• can be removed by TDICA.

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Comparison among Each ICA

• To investigate the relation between the filter
  length and source-separation performance of TDICA
  part in MSICA
• Comparison among separation performances of
  TDICA, FDICA, and MSICA

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Relation between Filter Length and Separation
Performance
9.4
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Comparison among Each ICA

• To investigate the relation between the filter
  length and source-separation performance of TDICA
  part in MSICA
• Comparison among separation performances of
  TDICA, FDICA, and MSICA

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Comparison Results
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Spectral Distortion (TDICA)
10 taps No whitening, 1000 taps whitening
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Spectral Distortion (FDICA, MSICA)
FDICA No whitening, MSICA No whitening
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Sound Demonstration of MSICA

• Reverberation time 300 ms
• Mixed speech (FemaleMale)
• Separated speech (Female)
• Separated speech (Male)

Female
Male
40
-30
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Conclusion

• Disadvantages of FDICA and TDICA
• Separation performance of FDICA is saturated
  before reaching a sufficient performance.
• Source separation using long filter fails in
  TDICA because the iterative rule for FIR-filter
  learning is complicated.
• MSICA combining FDICA and TDICA
• In TDICA part in MSICA, separation performance is
  improved even with the long filter.
• Separation performance of MSICA is superior to
  those of TDICA and FDICA.

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Future Work

• Further evaluation in real environment
• Robustness under reverberant conditions
• Larger array with more than 2-element
• To apply BSS to speech recognition system
• Improvement of convergence speed
• On-line and real-time algorithm

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ICA and BSS Where do we go?
We should go to NARA-city!
Why?
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4th International Symposium onICA and BSS
(ICA2003), in NARA

• Date April 1-4, 2003
• Place Nara, JAPAN
• Scientific Areas
• ICA and Factor Analysis, PCA etc.
• Blind source separation
• Blind and semi-blind equalization and
  deconvolution
• Blind identification
• Any signal processing application related with
  ICA
• URL http//ica2003.jp/

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Analysis Conditions
TDICA, TDICA part in MSICA
Filter length 102000 taps
Number of blocks B (Block length ) 110 (Data length/B)
ICA-iteration 500
FDICA part in MSICA
Number of subbands 1024 point
Frame shift 16 point
ICA-iteration 30
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Analysis Conditions
TDICA, TDICA part in MSICA
Filter length 10 (TDICA) 1000 (MSICA)
Number of blocks B 3 (TDICA) 9 (MSICA)
ICA-iteration 500
FDICA, FDICA part in MSICA
Number of subbands 1024 point
Frame shift 16 point
ICA-iteration 30