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Blind separation of underwater acoustic signals

TL;DR: A realistic model of an underwater acoustic channel is presented, then a general structure to separate acoustic signals crossing an underwater channel is proposed and some simulations have been presented and discussed.
Abstract: In last two decades, many researchers have been involved in acoustic tomography applications. Recently, few algorithms have been dedicated to the passive acoustic tomography applications in a single input single output channel. Unfortunately, most of these algorithms can not be applied in a real situation when we have a Multi-Input Multi-Output channel. In this paper, we propose at first a realistic model of an underwater acoustic channel, then a general structure to separate acoustic signals crossing an underwater channel is proposed. Concerning ICA algorithms, many algorithms have been implemented and tested but only two algorithms give us good results. The latter algorithms minimize two different second order statistic criteria in the frequency domain. Finally, some simulations have been presented and discussed.

Summary (2 min read)

I. INTRODUCTION

  • To estimate ocean physical parameters (such as temperature distribution, currents, sediment structure), The Ocean Acoustic Tomography (OAT) is widely used.
  • In active OAT, a typical sound source in known fixed position should be emitted.
  • These methods can be applied in many fields including speech processing, data communication, biomedical signal processing, radar, sonar as well as the surveillance and control of airport and sea traffic.
  • The authors apply BSS algorithms in PAT in order to improve and simplify the PAT algorithms as well as the processing of the received signals.

A. Acoustic Channel Model

  • Under some mild assumptions [12] , acoustic submarine channel can be considered as a multiple paths which, in frequency domain, each of them can be defined by a complex constant gain (i.e. a real lag i τ and a real gain C i ).
  • In the following, the authors assume that the channel is a linear and causal one and that the coefficients hij(z) are FIR filters.
  • The instantaneous case has been studied in [1] .
  • -After that, the same algorithm should be tested on simple mixture of acoustic signals.
  • In practise, their simulated underwater acoustic channel used the ray theory as a propagation model which is the more appropriate model to their application.

B. Acoustic Signals

  • Generally, Independent Component Analysis (ICA) algorithms use only the independence assumption of the sources.
  • In PAT applications, the sources are some signals of opportunities.
  • That study is of extreme important to ours.
  • In fact, according to the characterization study, one can conclude the following facts: -All the recorded signals have a background ocean noise which can be considered as an Additive White Gaussian Noise (AWGN).
  • -Many signals are Gaussians or close to Gaussians ones.

A. Background and Assumptions

  • The selected algorithms have been tested using the following three steps: -To valid their implementation, the authors use same (or similar) signals used by the authors of the algorithm, and they try to obtain same (or similar) results shown by the authors.
  • In their experimental studies, the authors found that at the third step none of the tested algorithms can unfortunately achieve a satisfactory separation according to a set of performance indexes [16] .
  • For this reason, a complete separation structure has been implemented using the following pre-and postprocessing modules of the signals see Fig.
  • -The filter bank is to improve the frequency resolution of the frequency algorithms.
  • In [2] , the authors used the following least-squares based joint diagonalization criterion for the case when a sample estimate of each is available: ) , ( m.

C. Convolutive Blind Separation of Non-Stationary

  • This algorithm will be called later "Parra".
  • The main difference between the two approaches remains on the considered estimation model.
  • The authors prefer instead of estimating a forward model B of H and finding a stable inverse to directly estimate a stable multi-path backward FIR model W.
  • They wish to find model sources with cross-powerspectral-density satisfying: EQUATION.

IV. EXPERIMENTAL RESULTS

  • In almost all the simulations, the separation of artificial or natural mixtures have been successfully achieved.
  • The authors should mention here, that good results have been obtained by only applying SOS algorithm except for some configurations notably when the sources are close to the water surface.
  • This index is forced to be zero for the mixture values and 1 for the sources.

V. CONCLUSION

  • The authors presented a general structure using BSS algorithms applied on a real word application which is the Passive Acoustic Tomography (PAT).
  • After many simulations, the authors obtained experimental results that showed the necessity of considering pre-processing and post processing which have to be applied to the observed signals in order to achieve properly the separation of the sources.
  • Many algorithms have been implemented and tested on their application but only few BSS algorithms dedicated to the separation of non-stationary signals gave satisfactory results.

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Blind Separation of Underwater Acoustic Signals
N. Benchekroun, and A. Mansour, Member, IEEE
Abstract- Acoustic tomography is an issue of great importance
in many applications. Few algorithms have been dedicated to
the passive acoustic tomography of a single input single output
(SISO) channel. As matter of fact, most of those algorithms can
not be applied in a real situation i.e. for a Multi-Input Multi-
Output (MIMO) channel. In this paper, we discussed at first
the features of the acoustic channel and signals then we
proposed an architecture to separate acoustic signals issued
from an acoustic realistic channel. The proposed structures
used algorithms based on independent component analysis
(ICA). We should mention here that many algorithms have
implemented and tested but only two algorithms give good
results. The latter algorithms minimize two different second
order statistic criteria in the frequency domain. Finally, some
simulations have been presented and discussed.
I. INTRODUCTION
To estimate ocean physical parameters (such as temperature
distribution, currents, sediment structure), The Ocean
Acoustic Tomography (OAT) is widely used. Acoustic
tomography is used in many civil or military applications
such as: Mapping underwater surfaces, meteorological
applications, Warfare. OAT basic principle relies on
dependence of the acoustic propagation on the spatial
distribution of the ocean parameters, in particular
temperature. Two kind of OAT can be used: Classical active
OAT and Passive ones. In active OAT, a typical sound
source in known fixed position should be emitted. At the
receiver, one can estimate the channel parameters by using
the properties of the received signal. Many algorithms [11,
12] have been developed to deal with active acoustic
tomography.
Recently, the Passive Acoustic Tomography (PAT) [10]
which is an acoustic tomography variant where the usual
cooperative acoustic source is replaced by a non-cooperative
noise source as for example a ship of opportunity, has taken
an increased importance because it exhibits three main
advantages: suits the Submarine Acoustic Warfare
Applications, avoids the need of both economically and
operationally expensive signal sources and allows the
investigation of areas as wide as those swept by the moving
ships and finally doesn’t perturb the ecological system. In
typically real world PAT applications, underwater signals
are generated by various sources in motion whose number’s
and positions are hardly identified. With more than two
sources, many actual tomography algorithms can’t give
pleasant results. Many others don’t work well or at all when
the emitted signals are large band [14].
The Blind Separation of Sources (BSS) problem consists on
retrieving unknown mixed independent sources from their
observed mixture. To reach that goal, researchers use
Independent Component Analysis (ICA) methods. Actually,
the last methods are ones of the most up-to-date methods in
signal processing. These methods can be applied in many
fields including speech processing, data communication,
biomedical signal processing, radar, sonar as well as the
surveillance and control of airport and sea traffic. In this
paper, we apply BSS algorithms in PAT in order to improve
and simplify the PAT algorithms as well as the processing of
the received signals.
II. ACOUSTIC CHANNEL MODEL AND
ACOUSTIC SIGNALS
A. Acoustic Channel Model
Under some mild assumptions [12], acoustic submarine
channel can be considered as a multiple paths which, in
frequency domain, each of them can be defined by a
complex constant gain (i.e. a real lag
i
τ
and a real gain C
i
).
For a classic Single Input Single Output (SISO) Channel, the
relationship between the emitted signal
, which will be
called later on as source signal and the received (or observed
signal
)
is given by:
)(ts
(tx
(1)
=
+=
M
i
ii
tntsCtx
0
)()()(
τ
Where n(t) stands for an Additive White Gaussian Noise
(AWGN) and M is the channel order or the number of paths.
In general case, the channel can be considered as Multiple
Input Multiple Output (MIMO) channel whose mathematical
model is given by the following equation:
(2)
=
+=
M
i
nNinSiHnX
0
)()()()(
Where
is the )(nX
1
×
q
vector of observed signals, is
the
)(nS
1
×
p
vector of sources, N(n) is a AWGN
1
×
q
vector
and H is the mixing system where H(z) = (h
ij(z)) is a
qp
×
complex polynomial matrix. In the following, we assume
that the channel is a linear and causal one and that the
coefficients h
ij(z) are FIR filters.
It is obvious that for PAT applications, Blind Source
Separation (BSS) problem can be very helpful. In BSS
terminology, the above problem can be solved by

considering the blind separation of linear mixed signals.
Linear mixtures include the following two models:
- Convolutive Mixtures: When the channel is a multi-path
with memory channel (i.e. an echo real channel). This type
of mixture can represent the general case of acoustic
underwater channel, see equation (2).
- Instantaneous Mixtures: this model is a simplified
convolutive one, especially when the channel is a memory-
less channel (without echo). The last case can be observed in
deep water environment. Then, equation (2) can be rewritten
as:
(3)
In our study, it is the general case (2) which will be
considered. The instantaneous case has been studied in [1].
Convolutive mixture algorithms are generally time
consuming algorithms. Few of them have been developed in
the literature [13] and are dedicated to specific tasks and
signals. In our knowledge, none of them has been optimized
to deal with our problem.
)()()( tNtHStX +=
- After that, the same algorithm should be tested on simple
mixture of acoustic signals.
In practise, our simulated underwater acoustic channel used
the ray theory as a propagation model which is the more
appropriate model to our application. In our model, a sand
bottom had been considered and some random coefficients
have been added to characterize varieties on the top and the
bottom of the channel. Finally, an acoustic model proposed
in [15] was used to consider the acoustic propagation effect.
B.
Acoustic Signals
Generally, Independent Component Analysis (ICA)
algorithms use only the independence assumption of the
sources. In PAT applications, the sources are some signals
of opportunities. Extensive experimental studies have been
conducted by a research engineer in our laboratory to
classify and characterize many recorded artificial (made by
human activities as boats, ships or submarine noises,etc.)
and natural (mainly animals sounds or noises) signals. That
study is of extreme important to ours. In fact, according to
the characterization study, one can conclude the following
facts:
- All the recorded signals have a background ocean noise
which can be considered as an Additive White Gaussian
Noise (AWGN).
- Many signals are Gaussians or close to Gaussians ones.
- Even if all the signals are non-stationary signals, some of
them have more or less periodic components as boat noises.
- Natural signals are very sparse ones and artificial ones are
very noisy.
The above mentioned properties were very useful to select
appropriate ICA algorithms.
III.
SEPARATION STRUCTURES APPLIED TO
ACOUSTIC SIGNALS
A.
Background and Assumptions
The selected algorithms have been tested using the
following three steps:
- To valid our implementation, we use same (or similar)
signals used by the authors of the algorithm, and we try to
obtain same (or similar) results shown by the authors.
- At the end, we try the algorithm on real signals which
cross our simulated underwater acoustic channel.
In our experimental studies, we found that at the third step
none of the tested algorithms can unfortunately achieve a
satisfactory separation according to a set of performance
indexes [16]. For this reason, a complete separation structure
has been implemented using the following pre- and post-
processing modules of the signals see Fig. 1:
- The Low Pass Filter helps us to reduce the impact of
AWGN.
- The filter bank is to improve the frequency resolution of
the frequency algorithms.
- The recovering module of the signals is based on second
order statistics and it uses the correlation of the signals in
time or frequency domain.
Fig.1. The proposed structure
Using these pre- and post-processings, we found that among
the tested algorithms, only two [2, 7] have given satisfactory
results. They were dedicated to separate non-stationary
sources (audio or music signals) and will be called in the
following SOS [2] and Parra [7]. Both of them are
implemented in frequency domain and are using discrete
frequency adapted filter.
B. A Frequency Domain Method For Blind Source
Separation Of Convolutive Audio Mixture (SOS)
K. Rahbar et al. in [2, 6] propose an algorithm which
minimize a criterion based on the cross-spectral density
matrix of the observed signals. For non-stationary signals,
the latter matrix depends of frequency and time epoch m:
Let
),( mP
x
ω
represent the cross-spectral density matrix of
the observed signal at frequency
ω
and time epoch m. Based

on the above assumptions, the main idea of this approach
comes from the following equation:
(4)
IHmPHmP
s
x
2
)(),()(),(
σωωωω
+=
+
Where
),( mP
s
ω
is a diagonal matrix which represents the
cross-spectral density matrix of the sources at epoch m and
is the power of N(t). In practise,
2
σ
ω
has to be discretized
as
K
k
k
π
ω
2
=
where K is the total number of frequency
samples. For q>p,
can be estimated from the smallest
eigenvalue of the matrix
. Therefore, we consider
the following noise free case:
2
σ
),(
~
mP
x
ω
(5)
)(),()(),(
ωωωω
+
= HmPHmP
s
x
To do so, the authors of [2] developed a two stages
algorithm. The first stage employs joint diagonalization [3,
4, 5] of the set of cross power spectral density matrices
, m = 0,…, M-1 at each frequency
),( mP
x
ω
k
ω
, over M
epochs, to estimate the mixing system up to a permutation
and diagonal scaling ambiguity at each frequency bin. In [2],
the authors used the following least-squares based joint
diagonalization criterion for the case when a sample estimate
of each
is available:
),( mP
x
ω
F
K
k
M
m
kkkkx
mB
BmBmP
k
∑∑
=
=
+
Λ
Λ
1
0
1
0
2
^
1)(),(
)(),()(),(min
ωωωω
ω
(6)
Where
)(
k
B
ω
is an estimate of the mixing system )(
k
H
ω
,
is a sample estimate of the observed signal
cross spectral density matrix at frequency bin
),(
^
mP
kx
ω
k
ω
and time
epoch m, and
),( m
k
ω
Λ is a diagonal matrix, representing
the unknown cross-spectral density matrix of the sources at
each epoch m. In the second stage of the algorithm, the
authors propose a novel solution for solving the permutation
problem which exploits the cross-frequency correlation
between diagonal values of
),( m
k
ω
Λ and ),(
1
m
k+
Λ
ω
.
Finally, having
)(
k
B
ω
= )(
k
H
ω
Π
D(
k
ω
) at each
frequency bin (
is a permutation matrix and
D(
pp
R
×
Π
k
ω
) represents a frequency-dependent diagonal matrix),
we can calculate the separating matrix
)(
k
W
ω
from the
following equation:
(7)
)()(
kk
BW
ωω
+
=
Where
) is the pseudo inverse of matrix
k
B
ω
(
+
)(
k
B
ω
.
C.
Convolutive Blind Separation of Non-Stationary
Sources (Parra)
The main idea of the algorithm [7] proposed by L. Parra and
C. Spence is similar to the previous ones [2] and [8]. This
algorithm will be called later “Parra”.
The main difference
between the two approaches remains on the considered
estimation model. The authors prefer instead of estimating a
forward model B of H and finding a stable inverse to
directly estimate a stable multi-path backward FIR model
W. They wish to find model sources with cross-power-
spectral-density satisfying:
(8)
)()],(),()[(),(
^^
ωωωωω
H
n
xs
WmmPWm Λ=Λ
A multipath model W that satisfies these equations for M
epochs simultaneously can be found with a Least Square
estimate:
2
11
1)(
,0)(
,,
^^^
),(minarg,,
∑∑
==
=
<<>=
ΛΛ
=ΛΛ
K
k
M
m
W
KQW
W
ns
mErW
ii
ns
ω
ω
ττ
(9)
Where
),()()],(),()[(),(
^
mWmmPWmEr
s
H
n
x
ωωωωωω
ΛΛ=
The additional time domain constraint on the filter size Q of
W relative to the frame size K, i.e.
0)( =
τ
W
KQ
<
<>
τ
will restrict the solutions to be continuous in the frequency
domain and solve the frequency permutation problem. The
same idea was used in [9].
IV.
EXPERIMENTAL RESULTS
Many simulations have been conducted. Generally, we need
over 600000-1200000 samples to achieve the separation.
The original sources are sampled at 44 KHz. In almost all
the simulations, the separation of artificial or natural
mixtures have been successfully achieved. In these
simulations, we have set the channel depth between 100 to
500m, the distances among the sources or the sensors are
from 30 to 300 m, the distances among the different sources
and the diverse sensors are from 1500 to 2500 m, the
number of sensors (3 in all the simulations) is strictly greater
than the number of sources (2).
Fig. 2 represents the experimental results obtained by
applying the structure (SOS) proposed in fig.1 to separate a
mixture of acoustic signals (Whale and ship). We should
mention here, that good results have been obtained by only
applying SOS algorithm except for some configurations
notably when the sources are close to the water surface. For
the latter cases, we found that the Parra algorithm before
SOS algorithm could improve the overall results.

Fig. 2. Experimental results: the first line shows respectively the original
and the estimated sources, the second line contains the observed signals (the
sources are: a whale sound and a boat noise)
Best results have been obtained when both algorithms Parra
and SOS are used and the number of sensors is strictly
greater than the number of sources, as shown in Fig3.
Fig.3. The general structure
Fig. 4 shows the experimental results obtained by applying
the general structure (Parra+SOS) proposed in fig.3 to
separate a mixture of acoustic signals (two ships) convolved
in an acoustic channel.
Fig. 4. Experimental results: The figure shows respectively the original, the
estimated sources at the first line and the observed signals at the second line
(the sources are: two boat noises).
Fig. 5
Fig. 5 shows the experimental results obtained by the
different algorithms (Parra, SOS or Parra + SOS) applied to
the same acoustic sources and the same configuration of the
acoustic channel at each simulation. In this figure, a
normalized performance index based on nonlinear
decorrelation is used [16]. This index is forced to be zero for
the mixture values and 1 for the sources.
V. CONCLUSION
In this paper, we presented a general structure using BSS
algorithms applied on a real word application which is the
Passive Acoustic Tomography (PAT). After many
simulations, we obtained experimental results that showed
the necessity of considering pre-processing and post
processing which have to be applied to the observed signals
in order to achieve properly the separation of the sources.
Many algorithms have been implemented and tested on our
application but only few BSS algorithms dedicated to the
separation of non-stationary signals gave satisfactory results.
Our future work consists on developing a BSS algorithm
which can use other features of acoustic signals.
REFERENCES
[1] Mansour, C. Gervaise, “ICA applied to passive oceanic tomography,”
WSEAS Trans. Acoustics and Music, Issue 2, Vol. 1, April 2004.
[2] K.Rahbar, James P. Reilly, “A new frequency domain method for
blind source separation of convolutive audio mixture,” IEEE trans.
Speech and audio processing, 2005.
[3] B.Flurry, W.Gautschi, “An algorithm for the simultaneous orthogonal
transformation of several positive definite symmetric matrices to
nearly orthogonal,” SIAM, vol.7, pp. 169 -184, 1986.
[4] J.F. Cardoso, A. Soulamic, “Blind Beamforming for non gaussian
Signals,” IEEE proceedings – F, page 362- , vol. 140, n° 6, Dec. 93
[5] Belouchrani, K. Abed-Meraim, J.F. Cardoso, “A blind separation
technique using second order statistics,” IEEE on Trans. Signal
Processing, vol. 45, pp. 434 - 444, Feb. 1997.
[6] K. Rahbar, J. Reilly, H. Manton, Blind identification of MIMO FIR
systems driven by quasi-stationary sources using second order
statistics: A frequency domain approach,” IEEE Trans. on Signal
Processing, vol. 52, pp. 406 - 417, February 2004.
[7] L. Parra, C. Spence, “Convolutive blind separation of non-stationary
sources,” IEEE Trans. Speech and Audio Processing, vol. 8, No. 3,
May 2000
[8] Capdevielle, C. Serviere, J.L. Lacoume, “Blind separation of wide-
band sources in the frequency domain,” In Proc. ICASSP 95, pp.
2080-2083, 1995.
[9] Mansour, M. Kawamoto, C. Puntonet, “A time-frequency approach to
blind separation of under-determined mixture of sources,”
International Conference of Applied Simulation and Modelling,
September 3-5, 2003, Marbella, Spain.
[10] D.Gaucher, C. Gervaise, G. Jourdain, “Feasability of passive oceanic
acoustic tomography in shallow water context: Optimal design of
experiments,” In European Conference on Under-water Acoustics
ECUA 2004, pages 56-60, Delft, Netherlands, 5-8 July 2004.
[11] Gervaise, A. Quinquis, I. Luzin, “High resolution identification of an
underwater channel from unknown transient stimuli,” In 18eme
Colloque Gresti, Toulouse, 10-13 Sept 2001.
[12] Gervaise, A. Quinquis, N. Martins, “Time frequency approach of
blind study of acoustic submarine channel and source recognition,” In
Physics in Signal and Image Processing, PSIP 2001, Marseille,
France, January 2001.
[13] Mansour, A. Kardec Barros, N. Ohnishi, “Blind separation of
sources: Methods, assumptions and applications,” IEICE
Transactions on Fundamentals of Electronics, Communications and
Computer Sciences, E83-A(8):1498-1512, August 2000.
[14] N. Martins, S. Jesus, C. Gervaise, A. Quinquis, “A time-frequency
approach to blind deconvolution in multipath underwater channels,”
In Proceedings of International Conference on Acoustics Speech and
Signal Processing 2002, ICASSP2002, Orlando, Florida, U.S.A, 13-
17 May 2002.
[15] M. Shulkin and H. W. Marsh, “Sound absorption in sea water,
Journal of the Acoustical Society of America, vol. 134, pp. 864–865,
1962.
[16] Mansour, “A survey of real world performance indexes of ICA
algorithms,” in preparation 2006.
Citations
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01 Jan 2007
TL;DR: A taxonomy is provided, wherein many of the existing algorithms for blind source separation of convolutive audio mixtures can be organized, and results from those algorithms that have been applied to real-world audio separation tasks are presented.
Abstract: In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks.

299 citations


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  • ...In these situations the sources are the desired signals, yet only the recordings of the mixed sources are available and the mixing process is unknown....

    [...]

Journal ArticleDOI
TL;DR: An alternative approach to multi-channel underwater signal enhancement is proposed that can improve the detection range of a passive acoustic detector five times on average (for input SNR between -10 and 5 dB) using only two receivers.
Abstract: A common problem in passive acoustic based marine mammal monitoring is the contamination of vocalizations by a noise source, such as a surface vessel. The conventional approach in improving the vocalization signal to noise ratio (SNR) is to suppress the unwanted noise sources by beamforming the measurements made using an array. In this paper, an alternative approach to multi-channel underwater signal enhancement is proposed. Specifically, a blind source separation algorithm that extracts the vocalization signal from two-channel noisy measurements is derived and implemented. The proposed algorithm uses a robust decorrelation criterion to separate the vocalization from background noise, and hence is suitable for low SNR measurements. To overcome the convergence limitations resulting from temporally correlated recordings, the supervised affine projection filter update rule is adapted to the unsupervised source separation framework. The proposed method is evaluated using real West Indian manatee (Trichechus m...

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TL;DR: A novel approach for solving the single-channel signal separation is presented the proposed sparse nonnegative tensor factorization under the framework of maximum a posteriori probability and adaptively fine-tuned using the hierarchical Bayesian approach with a new mixing mixture model.
Abstract: A novel approach for solving the single-channel signal separation is presented the proposed sparse nonnegative tensor factorization under the framework of maximum a posteriori probability and adaptively fine-tuned using the hierarchical Bayesian approach with a new mixing mixture model. The mixing mixture is an analogy of a stereo signal concept given by one real and the other virtual microphones. An “imitated-stereo” mixture model is thus developed by weighting and time-shifting the original single-channel mixture. This leads to an artificial mixing system of dual channels which gives rise to a new form of spectral basis correlation diversity of the sources. Underlying all factorization algorithms is the principal difficulty in estimating the adequate number of latent components for each signal. This paper addresses these issues by developing a framework for pruning unnecessary components and incorporating a modified multivariate rectified Gaussian prior information into the spectral basis features. The parameters of the imitated-stereo model are estimated via the proposed sparse nonnegative tensor factorization with Itakura–Saito divergence. In addition, the separability conditions of the proposed mixture model are derived and demonstrated that the proposed method can separate real-time captured mixtures. Experimental testing on real audio sources has been conducted to verify the capability of the proposed method.

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  • ...BSS is flourishing in numerous fields, including underwater signal processing [31], communication [27], speech enhancement [37], biomedical [14] and audio signal recognitions [42]....

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Proceedings ArticleDOI
10 Jun 2012
TL;DR: The weighted kernel k-means algorithm is modified according to the specific requirement of the permutation problem, and the spectral interpretation of the kernel approach is investigated and several kernel construction approaches to improving the permutations performance are proposed.
Abstract: In frequency domain blind source separation (FDBSS), separated frequency bin data in the same source must be grouped together before outputting the final result, which is the well-known permutation problem. Clustering techniques are broadly used in solving the permutation problem, however, some challenges still exist, for example, elongated datasets should be handled, and constraint from the background knowledge must be considered. Inspired by various successful applications of kernel and spectral clustering methods in machine learning and data mining community, we try to solve the permutation problem by these methods. In this paper, the weighted kernel k-means algorithm is modified according to the specific requirement of the permutation problem, and the spectral interpretation of the kernel approach is also investigated. In addition, we propose several kernel construction approaches to improving the permutation performance. Different experiments are carried out on a uniform platform, and show better performance of the proposed approach.

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Journal ArticleDOI
TL;DR: This study reviews the originality and development of the Brain Computer Interface (BCI) system and focus on the BCI system design based on Blind Source Separation (BSS) techniques.
Abstract: This study reviews the originality and development of the Brain Computer Interface (BCI) system and focus on the BCI system design based on Blind Source Separation (BSS) techniques. The study also provides the recent trends and discusses some of a new ideas for BSS techniques in BCI architecture, articles which discussing the BCI system development were analysed, types of the BCI systems and the recent BCI design were explored. Since 1970 when the research of BCI system began in the California Los Angeles University, the interest and the amount of research in BCI have been increased significantly; especially, when the BSS theory emerged in 1982 by a simple discussion between researchers. A lot of refereed journals and conference papers are reviewed and categorized to make this study in useful form. However, there are a few comprehensive reviews of BSS techniques in BCI literature. The review concludes with a brief discussion and expected future of the BCI.

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  • ...Wide applications of CBSS, in speech, music, underwater signals recorded in passive sonar, radio communications, antenna arrays, astronomical data, satellite images and interpret functional brain imaging data (Hansen and Dyrholm, 2003; Mansour et al., 2006; Pedersen et al., 2007)....

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References
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Journal ArticleDOI
TL;DR: An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time and may actually be seen as an extension of the principal component analysis (PCA).

8,522 citations


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  • ...It was proved that the output signals can be the sources up to a factor (or filter) scale and up to a permutation [7]....

    [...]

Journal ArticleDOI
01 Dec 1993
TL;DR: In this paper, a computationally efficient technique for blind estimation of directional vectors, based on joint diagonalization of fourth-order cumulant matrices, is presented for beamforming.
Abstract: The paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resort to their hypothesised value. By using estimates of the directional vectors obtained via blind identification, i.e. without knowing the array manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors etc., so that neither array calibration nor physical modelling is necessary. Rather suprisingly, ‘blind beamformers’ may outperform ‘informed beamformers’ in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption on which blind identification relies is the statistical independence of the sources, which is exploited using fourth-order cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalisation of fourth-order cumulant matrices; its implementation is described, and its performance is investigated by numerical experiments.

2,851 citations


"Blind separation of underwater acou..." refers methods in this paper

  • ...The first stage employs joint diagonalization [3, 4, 5] of the set of cross power spectral density matrices...

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Journal ArticleDOI
TL;DR: A new source separation technique exploiting the time coherence of the source signals is introduced, which relies only on stationary second-order statistics that are based on a joint diagonalization of a set of covariance matrices.
Abstract: Separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed. In many situations, no a priori information on the mixing matrix is available: The linear mixture should be "blindly" processed. This typically occurs in narrowband array processing applications when the array manifold is unknown or distorted. This paper introduces a new source separation technique exploiting the time coherence of the source signals. In contrast with other previously reported techniques, the proposed approach relies only on stationary second-order statistics that are based on a joint diagonalization of a set of covariance matrices. Asymptotic performance analysis of this method is carried out; some numerical simulations are provided to illustrate the effectiveness of the proposed method.

2,721 citations


"Blind separation of underwater acou..." refers methods in this paper

  • ...The first stage employs joint diagonalization [3, 4, 5] of the set of cross power spectral density matrices...

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors present state-of-the-art numerical techniques to solve the wave equation in heterogeneous fluid-solid media and present a comprehensive and modern introduction to computational ocean acoustics accessible to students.
Abstract: Senior level/graduate level text/reference presenting state-of-the- art numerical techniques to solve the wave equation in heterogeneous fluid-solid media. Numerical models have become standard research tools in acoustic laboratories, and thus computational acoustics is becoming an increasingly important branch of ocean acoustic science. The first edition of this successful book, written by the recognized leaders of the field, was the first to present a comprehensive and modern introduction to computational ocean acoustics accessible to students. This revision, with 100 additional pages, completely updates the material in the first edition and includes new models based on current research. It includes problems and solutions in every chapter, making the book more useful in teaching (the first edition had a separate solutions manual). The book is intended for graduate and advanced undergraduate students of acoustics, geology and geophysics, applied mathematics, ocean engineering or as a reference in computational methods courses, as well as professionals in these fields, particularly those working in government (especially Navy) and industry labs engaged in the development or use of propagating models.

1,344 citations

Journal ArticleDOI
TL;DR: This work tackles the problem of source separation by explicitly exploiting the nonstationarity of the acoustic sources, and finds an FIR backward model, which generates well separated model sources.
Abstract: Acoustic signals recorded simultaneously in a reverberant environment can be described as sums of differently convolved sources. The task of source separation is to identify the multiple channels and possibly to invert those in order to obtain estimates of the underlying sources. We tackle the problem by explicitly exploiting the nonstationarity of the acoustic sources. Changing cross correlations at multiple times give a sufficient set of constraints for the unknown channels. A least squares optimization allows us to estimate a forward model, identifying thus the multipath channel. In the same manner we can find an FIR backward model, which generates well separated model sources. Furthermore, for more than three channels we have sufficient conditions to estimate underlying additive sensor noise powers. We show the good performance in a real room environments and demonstrate the algorithm's utility for automatic speech recognition.

875 citations


"Blind separation of underwater acou..." refers background or methods in this paper

  • ...For the latter cases, we found that the Parra algorithm before SOS algorithm could improve the overall results....

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  • ...Using these pre- and post-processings, we found that among the tested algorithms, only two [2, 7] have given satisfactory results....

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  • ...This algorithm will be called later “Parra”....

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  • ...C. Convolutive Blind Separation of Non-Stationary Sources (Parra) The main idea of the algorithm [7] proposed by L. Parra and C. Spence is similar to the previous ones [2] and [8]....

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  • ...The main idea of the algorithm [7] proposed by L....

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Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "Blind separation of underwater acoustic signals" ?

In this paper, the authors discussed at first the features of the acoustic channel and signals then they proposed an architecture to separate acoustic signals issued from an acoustic realistic channel.