SINGLE CHANNEL SOURCE SEPARATION FOR CONVOLUTIVE
MIXTURES WITH APPLICATION TO RESPIRATORY SOUNDS
A. K. Kattepur
INRIA, Rennes, France
F. Jin
School of Electrical& Electronic Engineering, Nanyang Technological University, Singapore
F. Sattar
Faculty of Comp. Science and Infor. Tech, University of Malaya, Malaysia
Keywords:
Single channel, Blind Source Separation (BSS), Respiratory Sound (RS), Non-negative Matrix Factorization
(NMF).
Abstract:
In this paper, we attempt to extend single channel source separation techniques to the separation of respiratory
sound (RS) and heart sounds (HS). This single channel recording is analyzed and shown to be a convolutive
mixture model. After analyzing the reasons for failure of commonly used blind source separation algorithms,
we evaluate the efficacy of non-negative matrix factorization (NMF) techniques for this application. Analysis
on simulated single channel convolutive mixtures at various sensor positions has been performed. It indicates
an average signal to interference ratio (SIR) improvement of greater than 10 dB for the optimal sensor loca-
tions. The corresponding range of received power has been also studied for reliable separation of RS and HS.
Finally, the proposed model and the NMF separation performance are demostrated to work well on real RS
recordings.
1 INTRODUCTION
Single channel source separation is a problem with
considerable interests (Jang and Lee, 2003) where the
separation of multiple sources is performed from a
single channel recording. Compared to traditional
blind source separation (BSS) models (Choi et al.,
2005), this provides less diversity than the critically
determined case. When the convolutive mixtures are
involved, this problem becomes much more complex.
In the case of convolutive mixtures, the observed
signals are assumed to be combinations of delayed
and filtered versions of the independent components.
The task is to estimate the original sources without re-
sorting to a priori information about the mixing sys-
tem. In case of BSS, the prior assumptions of inde-
pendence and non-Gaussianity of the original signals
are used for the separation process (Choi et al., 2005).
In certain applications, only single sensor is pre-
ferred due to the ease of data acquisition, and the
sensor can only be positioned in one of the optimal
locations. For example, single channel recordings
of RS is vital for computerized pulmonary ausculta-
tion (Cort´es et al., 2005). Similarly, the single channel
HS recording play an important role in HS analysis
for the diagnosis of the heart valve dysfunction and
degeneration (Zhao and Wang, 2007). The optimal
microphone pick-up location depends on the applica-
tion and it is either on the suprasternal notch (tracheal
sounds), or over the left or right posterior base of the
lungs (lung sounds) (Sovij¨arvi et al., 2000). How-
ever, HS and RS show non-stationary behavior and
overlapping of frequency contents at all sensor loca-
tions (Charleston-Villalobos et al., 2006). Heart beat-
ing produces an intrusive quasi-periodic interference
that masks the clinical auscultative interpretation of
respiratory sound. Therefore, it is crucial to separate
both HS and RS signals effectively for accurate diag-
nosis.
Hence, we propose a convolutive mixing model
220
K. Kattepur A., Jin F. and Sattar F. (2010).
SINGLE CHANNEL SOURCE SEPARATION FOR CONVOLUTIVE MIXTURESWITH APPLICATION TO RESPIRATORY SOUNDS.
In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 220-224
DOI: 10.5220/0002712402200224
Copyright
c
 SciTePress

for the mixture of HS and RS. Simulated mixtures us-
ing different mixing indices have been then used to
verify the presented model. Finally, we compare the
techniques for separating convolutive single channel
mixtures based on real recorded sounds captured over
the chest and suprasternal notch for the extraction of
both clean HS and RS for clinical use.
2 FAILURE ANALYSIS OF
CONVENTIONAL BSS
ALGORITHMS
Algorithms typically used for BSS like JADE (Car-
doso and Souloumiac, 1993), FastICA (Bingham
et al., 2000), ACMA (Van der Veen and Paulraj, 1996)
and the time-frequency techniques like LI-TIFROM
(Abrard and Deville, 2005), have many applications
in multi-channel source separation. These include the
separation of communication, speech and audio sig-
nals.
However, when applied to single channel convo-
lutive mixtures, the above mentioned algorithms fail
due to various reasons as shown in Table 1. Therefore,
more specific BSS algorithms are required to sepa-
rate the single channel convolutive mixture of RS and
HS. The non-negative matrix factorization (NMF) al-
gorithm satisfying these criteria, thus becomes a suit-
able choice for this particular application.
Table 1: Failure Analysis of Common BSS algorithms.
Algorithm Failure Analysis
JADE
Unable to handle under-determined
mixtures. Unable to handle
convolutive mixtures.
FastICA
Unable to handle single source
mixtures. Deteriorated performance
for convolutive mixtures.
ACMA
Unable to handle under-determined
mixtures. Requires additional cons
tant modulus criterion. Deteriorated
performance for audio & speech
mixtures.
LI-TIFROM
Unable to handle convolutive mix
tures. Requires strict sparsity
criterion.
3 THE PROPOSED MODEL FOR
RESPIRATORY SOUNDS
Respiratory sounds being heard over the large air-
ways/chest are primarily related to vibrations of the
upper airway walls/chest and the turbulent airflow,
while heart sounds occur mainly due to the valvu-
lar activity of the heart. With an approximation,
the hypothetical sound sources of HS and RS can
be considered to have mutually uncorrelated point
sources (Kompis et al., 1998). RS can be acousti-
cally characterized by broad spectrum noise and the
presence of small time delay is related to the distance
between sound source and microphone (typically 0.03
ms) (Gavriely, 1999). The observed noisy RS signal
is considered to be a continuous RS signal interfered
by a discontinuous HS signal.
A reliable separation of the signals requires tak-
ing into account the structure of the mixing process.
In a real-life application, however, this process is un-
known, but some assumptions may be made about the
source statistics. In instantaneous mixing, the source
signals are assumed to arriveat the sensors at the same
time. This has been considered for separation of nar-
rowband signals with sampling frequency within few
hundred Hertz.
However, in real RS recordings, the RS and HS
signals arrive at the sensor through multiple paths and
therefore with different time lags. Furthermore, due
to the broadband nature of the RS, convolutive mix-
ing is suggested in this paper to model the real RS
recordings where observations can be considered as
the combinations of the unknown filtered versions of
the source signals. Under the assumption of anechoic
recording condition, the mixing process can be for-
mulated as:
x(k) =
N
∑
j=1
w
j
b
j
(k− l
j
) + v(k) (1)
where b
j
(k), x(k) and v(k) denote respectively the j
th
source signal, the observed signal and the noise cap-
tured by the sensor at time instance k. The attenua-
tion w
j
and the delay l
j
of the j
th
source to the sensor
would be determined by the physical position of the
source relative to the sensor.
4 NON-NEGATIVE MATRIX
FACTORIZATION (NMF)
The non-negative matrix factorization technique in-
troduced by (Lee and Seung, 1999), is able to produce
useful representations of real world data and can be
applied to the problem of single channel source sepa-
ration. The non-negative constraints usually required
for these class of algorithms are relaxed by making
use of standard ICA algorithms to zero-mean the ob-
served data. However, particular emphasis should
SINGLE CHANNEL SOURCE SEPARATION FOR CONVOLUTIVE MIXTURESWITH APPLICATION TO
RESPIRATORY SOUNDS
221

be given to the independence and sparsity of the ob-
served data.
Based on the observed single channel data x, the
NMF decomposes it into two basis matrices A and
S. This results in reduced representation of the origi-
nal data where each feature is a linear combination of
the original attribute set. The NMF has low compu-
tational complexity and unlike time-frequency tech-
niques, it is able to deal with both dense and sparse
data sets.
The NMF algorithm may be described in the fol-
lowing steps:
1. Initialize the elements of A and S to random non-
negative values. Normalize each column of A to
unit 2-norm.
2. Update the matrix A by either least squares or
Kullback-Leibler Divergence(KLD) as shown:
A ← A·
xS
T
ASS
T
(2)
A ← A·
x
AS
S
T
1· S
(3)
where ‘·’ is the element-wise multiplication oper-
ator and ‘−’ is the element-wise division opera-
tor. A values below an assigned threshold ε are
approximated to be zero. Normalize each column
of A to unit norm.
3. Update matrix S similarly as in step (2).
S ← S·
A
T
x
A
T
AS
(4)
S ← S·
A
T
x
AS
A· 1
(5)
4. Iterate steps (2) and (3) till convergence is
achieved.
The technique proposed by (Schmidt and Mørup,
2006) is based on 2D deconvolution and non-negative
matrix factorization (NMF). In order to successfully
separate convolutive mixtures, the NMF model is ex-
tended to the 2-dimensional case incorporating the
time τ and pitch φ of the signal.
x =
∑
τ
∑
φ
↓φ
A
τ
→τ
S
φ
(6)
where ↓ φ represents the downward shift operator
which moves each element of matrix φ rows down and
→ τ denotes the right shift operator which moves each
element in the matrix τ columns to the right. The least
squares and KLD approach for updating A and S are
then applied to separate the convolutive mixtures.
5 ANALYSIS AND RESULTS
5.1 Analysis on Simulated Data
5.1.1 Model Verification
In order to test the proposed convolutive mixing
model, single channel source separation was per-
formed on a mixture of tracheal/lung sounds and heart
sounds. Clean tracheal sound, lung sound, and heart
sound recordings from (Lehrer, 2002)(Wilkins et al.,
2004) are used as the source signals. The instanta-
neous and convolutive mixing process was performed
with specification from (MIT, 1999). Separation was
then performed using the LI-TIFROM and NMF tech-
niques. While LI-TIFROM can separate only instan-
taneously mixed sources, NMF can separate both in-
stantaneous and convolutive mixtures.
As seen from Fig. 1, the separation performance
of both algorithms is good in the case of instanta-
neous mixtures. However, the LI-TIFROM technique
is poor in the case of convolutive mixtures. This re-
sult, when extended to separation of respiratory and
heart sounds, provides interesting insights into the
modelling process. Since the LI-TIFROM technique
cannot separate even sparse mixtures of the recorded
signals, the mixing model must be convolutive. Even
though there are single source zones in the time-
frequency plane implying sparsity criterion, the LI-
TIFROM technique is unable to separate the real RS
recordings. So, the real recorded RS mixtures can be
modelled as a convolutive BSS problem.
5.1.2 Separation Performance
The separation performance of NMF which was con-
volutively mixed based on the specification in (MIT,
1999) was tested based on the signal to interference
ratio (SIR) improvement. This is given by:
SIR = 10log
10
ks
target
k
2


e
interf


2
(7)
where s
target
is the target signal and e
interf
is an al-
lowed deformation of the sources which accounts for
the interferences of the unwanted sources.
In order to test the separation performance of the
NMF algorithm, the scenario presented in Fig. 2 was
used. For each symmetric location of the sensor in the
(x, y) plane, the received power of the single channel
mixture was captured. This was then separated us-
ing the NMF algorithm and the average SIR improve-
ment was measured. As shown in Fig. 2, two cases
are analyzed including placing the sensor away from
both the sources (Case A) and in between the sources
BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing
222

0 2 4 6 8 10
x 10
4
−1
0
1
(a)
0 2 4 6 8 10
x 10
4
−0.5
0
0.5
(b)
0 2 4 6 8 10
x 10
4
−1
0
1
(c)
0 2 4 6 8 10
x 10
4
−0.5
0
0.5
(e)
0 2 4 6 8 10
x 10
4
−1
0
1
(d)
Magnitude
0 2 4 6 8 10
x 10
4
−1
0
1
(f)
Magnitude
0 2 4 6 8 10
x 10
4
−0.5
0
0.5
(g)
0 2 4 6 8 10
x 10
4
−1
0
1
(i)
0 2 4 6 8 10
x 10
4
−1
0
1
Samples
(h)
0 2 4 6 8 10
x 10
4
−0.2
0
0.2
Samples
(j)
Figure 1: (a) Single-channel instantaneous mixture; (b)
Single-channel convolutive mixture; LI-TIFROM sep-
arated signals for (c),(d) instantaneous mixture and
(e),(f)convolutive mixture; NMF separated signals for
(g),(h) instantaneous mixture and (i),(j) convolutive mix-
ture.
0
1
2
3
4
5
6
7
8
9
10
0
2
4
6
8
10
0
1
2
3
4
5
6
7
8
9
10
Distance
Distance
Distance
Source 1
Source 2
Sensor Position
Case A
Case B
0.5
Figure 2: Scenario used for modelling single channel source
separation.
(Case B). The tracheal and lung sounds have been
analyzed as separate sources with interference from
heart sounds in each scenario. As seen in the Figs.
3 and 4, the SIR improvements are superior when
the sensor position is far away from both the sources.
Similarly, the SIR improvementsare superior midway
between both the sources. When compared to the re-
ceived power in each case, a power level of less than
−5 dB indicates optimal separation performance. The
corresponding received power can be used as a look-
up graph for the selection of optimum sensor location
during the actual recording of RS.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
−20
0
20
40
Received
Power (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
10
20
Average SIR
Improvement (dB)
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
−20
0
20
Received
Power (dB)
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
0
5
10
15
Sensor Position
Average SIR
Improvement (dB)
Figure 3: Received power and SIR improvement for a mix-
ture of tracheal and heart sounds. The top two figures refer
to sensor positions in case A, while the bottom two figures
refer to case B.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
−50
0
50
Received
Power (dB)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0
10
20
30
Average SIR
Improvement (dB)
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
−20
0
20
40
Received
Power (dB)
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
0
10
20
Sensor Position
Average SIR
Impovement (dB)
Figure 4: Received power and SIR improvement for a mix-
ture of lung and heart sounds. The top two figures refer
to sensor positions in case A, while the bottom two figures
refer to case B.
5.2 Analysis on Real RS Recordings
5.2.1 Data Acquisition
Real RS recordings were done in anechoic room with
the subjects in sitting position. Single electret con-
denser microphone(ECM-77B, Sony Inc., Japan) was
inserted into a hemispherical rubber chamber of 2 cm
in diameter, and was placed over suprasternal notch.
The recordingenvironmentand equipmentswere cho-
sen based on the standard given by (Sovij¨arvi et al.,
2000). The choice of microphone together with the
recording condition, the environmental noises were
suppressed to the largest extend. Recording software
WAVEPAD (V3.05, NCH Swift Sound Software) was
used and the respiratory sound recordings have been
saved as mono-channel ‘*.wav’ files with sampling
SINGLE CHANNEL SOURCE SEPARATION FOR CONVOLUTIVE MIXTURESWITH APPLICATION TO
RESPIRATORY SOUNDS
223

frequency F
s
=11.025 kHz. Test subjects were asked
to breathe normally with no targeted flow. The char-
acteristics due to sex, age, weight were not taken into
consideration.
5.2.2 Evaluation
To evaluate the effectiveness of the NMF based tech-
nique, the separation performance are tested on sin-
gle channel separation of heart and breath sounds. As
shown in Fig. 5, the separation performance is quite
good and is shown to pass the subjective test for sepa-
ration. This proves that the proposed model and asso-
ciated parameters are consistent with those required
for separating the real recorded data.
0 0.5 1 1.5 2 2.5 3
x 10
5
−0.2
−0.1
0
0.1
0.2
(a)
0 0.5 1 1.5 2 2.5 3
x 10
5
−1
−0.5
0
0.5
1
(b)
Magnitude
0 0.5 1 1.5 2 2.5 3
x 10
5
−1
−0.5
0
0.5
1
Samples
(c)
Figure 5: Single channel source separation using NMF. (a)
Observed signal; (b) Separated HS; (c) Separated RS.
6 CONCLUSIONS
Non-negative matrix factorization techniques are
shown to perform well in case of single channel
source separation. The convolutive mixing model for
respiratory sounds has been verified based on the sep-
aration performance. The NMF technique, when used
on respiratory sounds, provides an SIR improvement
of over 10 dB for optimal sensor positions. This, on
the other hand, suggests an optimal sensor position
for sound capturing. Due to the good separation per-
formance, this has potential medical applications for
accurate detection of pulmonary and heart diseases
based on the separated RS and HS respectively.
REFERENCES
Abrard, F. and Deville, Y. (2005). A time-frequency blind
signal separation method applicable to underdeter-
mined mixtures of dependent sources. Signal Process-
ing, 85(7):1389–1403.
Bingham, E., Hyvrinen, A., and rinen, A. H. (2000). A
fast fixed-point algorithm for independent component
analysis of complex valued signals. Int. J. of Neural
Systems, 10:1–8.
Cardoso, J. F. and Souloumiac, A. (1993). Blind beam-
forming for non Gaussian signals. IEE Proceedings,
140(6):362–370.
Charleston-Villalobos, S., Aljama-Corrales, A. T., and
Gonzalez-Camarena, R. (2006). Analysis of simu-
lated heart sounds by intrinsic mode functions. Proc.
of 28th IEEE EMBS Conf., pages 2848–2851.
Choi, S., Cichocki, A., Park, H. M., and Lee, S. Y. (2005).
Blind source separation and independent component
analysis: A review. Neural Information Processing -
Letters and Reviews, 6(1):1–57.
Cort´es, S., Jan´e, R., Fiz, J. A., and Morera, J. (2005). Mon-
itoring of wheeze duration during spontaneous respi-
ration in asthmatic patients. Proc. 27th IEEE EMBS
Conf.
Gavriely, N. (1999). Automatic detection and analysis of
breath sounds. Eur. Patent, (EP 0 951 867 A2).
Jang, G.-J. and Lee, T.-W. (2003). A maximum likelihood
approach to single-channel source separation. J. Ma-
chine Learning Res., 4:1365–1392.
Kompis, M., Pasterkamp, H., Motai, Y., and Wodicka, G. R.
(1998). Spatial representation of thoracic sounds.
Proc. 20th IEEE EMBS Conf., pages 1661–1664.
Lee, D. and Seung, H. (1999). Learning the parts of ob-
jects by non-negative matrix factorization. Nature,
401(6755):788–791.
Lehrer, S. (2002). Understanding Lung Sounds. Philadel-
phia, PA: Saunders, Audio CD.
MIT (1999). ICA Synthetic Benchmarks.
Schmidt, M. N. and Mørup, M. (2006). Nonnegative ma-
trix factor 2-D deconvolution for blind single channel
source separation. In Int. Conf. on ICA and Signal
Separation.
Sovij¨arvi, A. R. A., Vanderschoot, J., and Eavis, J. R.
(2000). Standardization of computerized respira-
tory sound analysis. European Respiratory Review,
10(77):585–649.
Van der Veen, A. J. and Paulraj, A. (1996). An analytical
constant modulus algorithm. IEEE Trans. Signal Pro-
cessing, 44(5):1136–1155.
Wilkins, R. L., Hodgkin, J. E., and Lopez, B. (2004). Fun-
damentals of Lung and Heart Sounds. Mosby, Audio
CD.
Zhao, Z. D. and Wang, Y. (2007). Analysis of diastolic
murmurs for coronary artery diseasebased on hilbert
huang transform. Proc. of Int. Conf. Machine Learn-
ing and Cybernetics, 6.
BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing
224