Blind source separation based on acoustic pressure distribution and normalized relative phase using

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Blind source separation based on acoustic
pressure distribution and normalized relative
phase using dodecahedral microphone array

• Motoki Ogasawara
• Takanori Nishino
• Kazuya Takeda
• Nagoya University, Japan

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Introduction

• BACKGROUND
• Extracting sound sources, estimating their source
  directions
• Important techniques for many applications
• Tele-conference systems
• Selective listening point audio system Niwa
  2008
• Requires many microphones or microphone arrays
• PURPOSE
• Small and easy to set up microphone array
  device of high accuracy
• Development of a small dodecahedral microphone
  array device
• 8-cm diameter
• Propose a method to solve the permutation
  problem in FD-ICA using developed device.
  

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Dodecahedral microphone array
Distance between microphones 7 mm
Omnidirectional microphone(SONY ECM-77B)
Top face
8-cm diameter
Front face
60 microphones are mounted.

• FEATURES
• 1) Distance between microphones on each face is
  small (7 mm).
• Phase difference at high frequency can be
  distinguished more accurately.
• 2) Consists of flat faces, and sound-wave
  attenuation among faces is large.
• Large difference of sound pressure among
  different faces at low frequency.
• 3) Easy to set up and carry (8-cm diameter).

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Comparison with conventional microphone array

• CONVENTIONAL MICROPHONE ARRAY
• To obtain a large difference of sound pressure,
  larger distance between microphones or microphone
  arrays is need.
• The spatial aliasing occurs,and set up is
  difficult.
• To consider spatial aliasing, the distance
  between microphones or microphone arrays must be
  smaller.
• Difference of sound pressure is small.
• DEVELOPED MICROPHONE ARRAY
• Difference of sound pressure is large, even
  though the developed device has a small
  structure.
• Spatial aliasing does not occur, because the
  distance between microphones on each face is
  small.
• Array is compatible, both with spatial aliasing
  and with the difference of sound pressure.

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Acoustic pressure distribution

• Acoustic pressure distribution observed on the
  surface of the dodecahedral microphone array
• Distributions obtained corresponding to each
  source signal
• Difference of the sound pressure is larger than
  that in the spherical microphone array
  Remarkable feature of the flat face structure

Dodecahedral microphone array
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Angular difference distribution

• Angular difference distribution observed on the
  surface of the dodecahedral microphone array
• Note one of the faces

Spatial aliasing does not occur because the
distance between the microphones on each face is
small.
One face
Microphone
Easily obtains amplitude and phase difference.
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Human beings sound localization cue

• Relating the device's features with human beings
  sound localization cues.

Acoustic pressure lowArrival time
slow
Acoustic pressure high Arrival time
fast

• Using the information obtained by both ears
• Low frequency interaural time difference (ITD)
  phase feature
• High frequency interaural level difference (ILD)
  amplitude feature
• Amplitude and phase weights are different at low
  and high frequency.
• Concept of this weight is included in our
  proposed method.

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Outline of entire separation process
Dimension reduction by principal component
analysis (PCA)
Separated in each frequency using separation
filter w ( f )
Observed signals
Subspace signals
Subspacemethod(PCA)
STFT
FD-ICA
Scaling(Projection back)
Dodecahedral microphone array
Permutation problem occurs
Proposed method permutation alignment
Acoustic transfer function w( f ) (Frequency
response from the sound source
to the microphone)
w( f ) are clustered by k-means
algorithm.(Proposed similarity measure is used.)
Solving thepermutation problem at each frequency
Calculated by the pseudo-inverse of the
separation filter, w ( f )
Resultant separated signals
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Clustering method of acoustic transfer function

• Evaluated whether separated sources i and j ,
  which originate in each acoustic transfer
  function, are identical sound sources.
• Evaluation of the similarity of acoustic transfer
  function wi and wj.
• Example 3 microphones

Acoustic transfer function wj
Acoustic transfer function wi
Source sj
Source si
wi,1
Transfer function wj
Transfer function wi
Transfer function from source i to microphone 1
Microphone array
Evaluated whether a transfer functionoriginated
from identical sound source
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Similarity measure (Conventional method)

• Similarity measure is necessary to evaluate the
  similarity of the acoustic transfer function.
• CONVENTIONAL METHOD Sawada 2006
• Absolute value of the amplitude and the
  angular difference are evaluated by the
  Euclidean distance in the complex plane.
• This method evaluates the amplitude and the
  phase by the same weight.
• PROPOSED METHOD
• Amplitude and phase features are divided.
• Weighting function depends on the frequency is
  used.

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Similarity measure (Proposed method)

• Used for acoustic transfer function clustering
• Defined as a weighted sum
• Similarity of transfer function w( f ) and
  centroid ck
• Weighting function a( f ), b( f )
• High frequency
• big weight of the amplitude
• Low frequency
• big weight of the phase

k cluster index, f frequency index
Similarity of theamplitude feature
Similarity of thephase feature
Weight of the amplitude a Weight of the
phase b
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Similarity measure Simamp

• Similarity of an amplitude feature is evaluated
  by similarity measure Simamp .

Acoustic pressure distribution p(wi )
Normalization Summation of the absolute valued
amplitude is made one.
wi,1
wi,2
wi,3
Absolute value
Acoustic pressure distribution p(wj )
wj,1
1 2 3
Microphones
Evaluate by the Euclidean distance. (Total
amount of the differences is the amplitude
similarity.)
wj,2
wj,3
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Similarity measure Simphase

• Similarity of the phase feature is evaluated by
  Simphase.

• Inner product of complex vectors calculated

Transfer function wi and wj
Normalized phase feature f (wi ) and f
(wj )
I m
wi,1
q2
wj,2
q1
wj,1
wi,2
wi,3
Re
Phase feature calculated
q3
wj,3
Normalization Removing the frequency
dependency
This value is similarity of phase feature.
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Sound source separation experiments

• Comparison with the conventional method and the
  ideally solved permutation problem condition
• Source locations are unknown number of sources
  is known

Conditions
Setup (12 sources)
Source signal
Reverberation time 138 msec (soundproof chamber)
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Results of the speech signals
? Observed signal (12 sources) ? Separated
signal (Female 1)
SIR improvement score dB
Number of sources
Ideal Proposed Conventional

• Proposed method almost equals the ideal
  condition, up to six sources.
• Proposed method obtained a larger score than the
  conventional method.

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Results of the musical instruments signals
? Observed signal (4 sources) ? Separated
signal (Drums)
SIR improvement score dB
Song 1(6 sources)
Song 2(6 sources)
Song 3(4 sources)
Song 4(4 sources)
Ideal Proposed Conventional

• Proposed method outperformed conventional
  method in both the speech and musical
  instrument conditions.

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Summary and future works

• Summary
• Developed dodecahedral microphone array
• Proposed a novel method of solving the
  permutation problem using our developed array
• Developed array and method effectively separated
  source signals better than the conventional
  method.
• Future works
• Evaluation of separation performances under
  reverberant conditions
• Investigation of the estimation method for the
  number of sources in dimension reduction