J. Biomedical Science and Engineering, 2013, 6, 152-164 JBiSE
http://dx.doi.org/10.4236/jbise.2013.62019 Published Online February 2013 (http://www.scirp.org/journal/jbise/)
Processing obstructive sleep apnea syndrome (OSAS) data
Ren Sin Tung, Wai Yie Leong
Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia
Email: hotohori_sin@hotmail.com, waiyie@ieee.org
Received 4 March 2012; revised 5 November 2012; accepted 12 November 2012
In this study, the EEG signals were processed. Thir-
teen ICA algorithms were tested to verify the per-
formance efficiency. The EEG signals were recorder
using 10/20 international system, based on a 20 min-
ute sleep recording of a severe Obstructive Sleep Ap-
nea Syndrome (OSAS) during NREM and REM sleep.
Seven channels were used to record the EEG signals
which are sampled at 100 Hz. The performance analy-
sis of the algorithms were investigated to eliminate
the loss of the informative EEG signal during the data
processing. The denoising results were magnified with
the purpose of evaluating the robust ness of the de-
noising algorithms. From the result we obtained, we
are able to understand the denoising algorithm is
more suitable to process the EEG signal with lower
Keywords: E EG; Obstructive Sleep Apnea Syndrome
(OSAS); Independent Component Analysis (ICA);
Wavelets Analysis
Brain acts as the central of control and data processing
unit for the biological medium in a human. In order for
the brain cells to communicate to each other, the brain
uses action potential for the neural activity. With the
generation of action potentials by the brain cells, we are
able to record this minute activity by means of electrodes,
as in electroencephalogram (EEG).
With the advancement of technology, the ability to
measure the electrical activity using EEG has been im-
proved. Nowadays EEG technology is an inexpensive
and yet accurately measurement of brain wave activity at
the outer layer of the brain. Sensitive electrodes are at-
tached to the skull of the human and the signals are re-
corded in either unipolar or bipolar fashion.
The depolarization signals from the brain cells are at-
tenuated while passing through the connective tissues in
the brain structures, the brain fluid and the scalp, which
have complex impedances. In order to prevent collecting
noisy signal from the scalp, the skull need to be prepared
for a quality contact with the reason of overcoming the
impedance mismatch created by the hair and dead skin
on the head [1] .
In EEG recording, the positioning of the electrodes is
according to the International 10/20 system, shown in
Figure 1, which is an internationally recognized method
to describe and apply the location of scalp electrodes in
the context of an EEG test or experiment. Therefore, the
electrodes record overlapped brain activity transmitted
by volume conduction from different dynamic neocorti-
cal processes.
An example of normal EEG is shown in Figure 2
whereby the brain activities are recorded by a normal
adult male with his eyes closed during the EEG re-
cording. The EEG result shows a good alpha activity at
P3/P4, O1/O2.
While the EEG is able to record useful brainwave, it
can also record other signals such as noise or artifacts
which supposed to be independent from the brain activi-
ties. The noise or artifacts will overlap with neural brain
activities and it increases the difficulty in the EEG inter-
pretation. One current hypothesis which we usually re-
ferred to is that the artifacts are independent from brain
activity, either in normal or pathologic condition. With
this hypothesis and considering the signals are non-
Gaussian, a frequent method used to remove the noise is
Figure 1. 10/20 System EEG.
R. S. Tung, W. Y. Leong / J. Biomedical Science and Engineering 6 (2013) 152-164 153
Figure 2. Normal adult male of EEG, eyes closed, showing good alpha activity at P3/P4, O1/O2.
the blind source separation. However, Independent Com-
ponent Analysis (ICA), which is a class of blind source
separation, has proven capable of separating the artifacts
from the brain sources. Of the variety of ICA algorithms
available, which is more efficient in processing the EEG
data [2,3].
Independent Component Analysis (ICA) is a popular
technique that used widely for separating the noise or
artifacts from the EEG signals. ICA technique not only
able to separate the brain activities from non-brain ac-
tivities, it is also used to study the brain activities by an
EEG analyst in order to determine the brain disorders.
By using ICA as a tool to blindly separate overlapping
EEG signals and artifacts into independ en t sources, on e’s
is able to perform elimination on the unwanted signal
such as noise or artifacts and reconstruct the noiseless
EEG recording which is then used for diagnosing the
brain disorder [2].
A great challenge in biomedical engineering is to provide
a non-invasive method to assess the physiological chan ges
occurring in different organs of the human body. With
the recorded variation as the biomedical source signals,
the function or malfunction of various physiological sys-
tems are able to model and measure. As the biomedical
source signals are usually weak, nonstationary and dis-
torted by artifacts, signal processing techniques have
become an important role for analyzing the recorded
Besides the classical signal analysis tools (e.g. adap-
tive supervised filtering) are used to process the super-
imposed biomedical source signals, Intelligent Blind Sig-
nal Processing (IBSP) techniques such as blind source
separation is used with the aim of recovering independ-
ent sources given only sensor observations (linear mix-
ture of independent source signals). Roughly speaking,
the blind source separation can be formulated as the
problems of separating or estimating the waveform of the
original sources without knowing the parameters of mix-
ing [4].
Independent Component Analysis (ICA) is very clo se ly
to the blind source separation (BSS) or blind signal sepa-
ration. ICA is one method, perhaps the most widely used
in signal processing, for performing the blind source
separation. It is a way to obtain a linear transformation of
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R. S. Tung, W. Y. Leong / J. Biomedical Science and Engineering 6 (2013) 152-164
the measured signals such that the resulting source sig-
nals are statistically independent from each other.
To generally define ICA, statistical “latent variables”
model is used for the definition. Assuming the observed
linear mixtures 1,,
x of n independent components:
112 2,for all.
jj jjnn
as asasj  (1)
By leaving the time index t in the ICA model, each
mixture xj as well as each independent component sk is
assumed to be a random variable instead of a proper time
signal. The observed values xj(t) are then a sample of this
random variable. Without the loss of generality, both th e
mixture variables and the independent components are
assumed to be zero mean .
For the convenient purpose, vector-matrix notation is
used instead of the sum like in the Equation (1). The
random vector of x is denoted by the mixtures 1,,
and the random vector of s is denoted by the elements
s. Let us then denote A matrix with the elements
of aij whereby the bold lower case letter indicates vector
and bold upper case letter denote matrices. By using the
vector-matrix notation, the above mixing model is writ-
ten as
xAs (2)
The statistical model in Equation (2) is known as in-
dependent component analysis or ICA model. The ICA
model is a generative model whereby it describes how
the observed data are generated by a process of mixing
the components si. In this ICA model, the independents
are latent variables, meaning they cannot be observed
and the mixing matrix is assumed to be unknown. Ran-
dom vector x is observable and this is done under general
For a random noisy vector x(k), the mixing ICA model
can be represented as:
 
kkvxHs k
where H is an (m x n) mixing matrix,
 
ksksk sk
is a source vector of
statistically independent signals (unknown nonsingular
mixing matrix), is a
 
vkv kvkvk
vector of uncorrelated noise (addictive noise).
The purpose of the ICA is to formulate a linear trans-
formation W of the dependent sensor signals x that mak e
the output as indep endent as possible,
yk Wxk WAsk
where y is an estimate of the sources (independent com-
ponents) and the sources are exactly recovered when the
W is the inverse of the A.
From Equation (2), there is an ambiguities present in
the ICA model. The ambiguity that present in the Equa-
tion (2) is that we cannot determine the variances (ener-
gies) of the independent components. The reason for the
ambiguity is that both s and A being unknow n. Any sca-
lar multiplier in one of the sources si could always be
cancelled by dividing the corresponding column ai of A
by the same scalar. However, this ambiguity is, fortu-
nately, insignificant in most application. Besides that,
obtaining an exact inverse of the A matrix in most cases
is impossible. Thus, the source separation algorithms aim
to find a W matrix such as the product of WA in order to
permute the diagonal and scalar matrix [4-8].
In the last 20 years, different types of algorithms were
proposed and most of the algorithms proposed that the
sources are stationary and are based implicitly on high
order statistic (HOS) algorithms. With the application of
HOS algorithms, Gaussian sources cannot be separated
as they do not have higher than two statistic moments
while the second order statistic do not have such con-
straint. On the other hands, Second Order Statistics (SOS)
algorithm uses non stationary structure of the signals
(time or frequency structure) for the separation purpose.
Temporal, spatial and spatio-temporal decorrelations
play important roles in th e EEG signal analysis and these
techniques are based on the SOS algorithm. Furthermore,
they are the basis for the modern subspace methods of
array processing and frequently used to eliminate redun-
dancy or to reduce noise. In the spatial decorrelation
(pre-whitening) technique, the ICA tasks will usually
become easier and well-posed (less ill-conditioned) as
the unmixing system is described by an orthogonal ma-
trix for real-valued signals and a unitary matrix for com-
plex-valued signals and weights. With the same SOS,
one’s can compute different whitening transformation for
nonstationary sign als. Moreover, the spatio-temporal and
time delayed decorrelation can be used to identify the
mixing matrix and to perform blind source separation
which mainly on coloured source [2]. In contrast to the
correlation-based transformation such as principal com-
ponent analysis (PCA), ICA not only be able to decorre-
late the signals (second order statistic), but it can also
reduce higher order statistical dependencies in order to
generate signals as independent as possible [3,4,9].
2.1. SOBI Algorithm
One of the well-known second order based technique
that used to compute the separating matrix is called Sec-
ond Order Blind Identification (SOBI) algorithms. In the
SOBI algorithm, the separation of the matrix is achieved
in two steps. First step is the whitening the observed
signal vector by linear transformation, which is also
known as whitening matrix. Second step is applied the
Joint Approximate Diagonalization (JAD) on a set of
different time-delay correlation matrices of the whitened
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R. S. Tung, W. Y. Leong / J. Biomedical Science and Engineering 6 (2013) 152-164 155
signal vector. Since the whitening matrix is estimated
based on the noisy observed data, it highly suffers from
bias if the SNR is relatively low, especially if the noise
correlation matrix is unknown. Besides that, the Joint
Approximate Diagonalization (JAD) also suffers from
highly time correlated noise. In such cases, the correla-
tion matrices of the observed signals at nonzero time-
delay are still biased by unknown noise correlation ma-
trices. In order to overcome the bias of the whitening
matrix in white noise cases, robust SOBI algorithm has
been developed to overcome the weakness of SOBI al-
gorithm [10,11].
2.2. Robust SOBI Algorithm
The robust SOBI (SOBI-RO) algorithm formulates a new
correlation matrix as a weighted linear combination of a
set of time-delayed correlation matrices of the observed
signal vector. The weight linear combination is com-
puted in an iterative procedure th at makes the formulated
correlation matrix in positive define. The positive define
correlation matrix is used for computing the whitening
matrix and thereby whitening the observ ed signal vector.
In the robust SOBI algorithm, it combines robust whit-
ening and time-delayed decorrelation with the purpose of
improving the classical SOBI algorithm. By integration
the robust whitening instead of simple whitening, the
main objective of using robust whitening is to eliminate
the influence of whit e noi se [ 11] .
Recall the equation introduced in (3), the source sig-
nals s are assumed to be mutually uncorrelated and tem-
porally correlated (instead of independents) in a second
order statistic framework. Computation on this model
can be difficult as the presence of noise will influence
the correlation between signals. Hence its covariance
matrix at lag 0, can be a full
 
RE nknk
matrix which is unknown and the time-delayed correla-
tion matrix will become
 
Ri Enknki
null. With the above assumption, the correlation matrices
of the observation have:
 
RExk xkARAR (5)
 
RiExkxkiARiA R (6)
The first step (robust whitening) consists of finding a
matrix Q that correlates the signals in x for small time
lags. With the helping of ICALAB implementation,
which exploits Equation (6) for a single time lag i =1.
The matrix Rx(1) is then diagonalized by an eigen-de-
RUλλU (7)
The whitening matrix Q is then obtained from eigen-
vectors matrix Uc and forming a diagonal eigen-valeus
diag T
With the formation of Q matrix, the whitened signal z
ki Qxki for different time lags can be calcu-
lated. (The default option in ICALAB is 100 time lags).
The second step of robust SOBI is the same as the
classical SOBI, namely approximate joint diagonaliza-
tion of different Rz(i) matrices, computed with the Equa-
tion (6). Finally, the separation matrix W is give n by
WAQ (9)
where the matrix Q has been computed in the previous
whitening or orthogonalization step. Based on the fact
that A is an orthogonal matrix and the sources are spa-
tially uncorrelated [4,10-12].
2.3. Wavelet Denoising
In a real EEG recording, the recorded signals not only
contaminated with ocular or muscular artifacts, it is also
contaminated with noises that come from different sources.
Currently, in order to remove the noise from the non-
stationary signals, Wavelet Denoising (WD) is usually
applied for improving the separation result. In WD, the
recorded signals are decomposed on wavelet basis. After
that, we are able to obtain a representation of the signal
that concentrate most of its energy in few wavelet coeffi-
cients which having large ab solute values. In the wavelet
denoising process, the noise energy distribution does not
change, which mean that its energy will not be hold by
large value of coefficients. By using large coefficients
for denoising, it will lead to an almost noise-free signal.
The main problem is the computation of the threshold,
which mean responding to where to fix the boundary
between the small and large wavelet coefficient?
There are a few algorithms have been proposed in the
past years and the most well known algorithm is known
as Donoho’s universal thresholding. The Donoho’s uni-
versal thresholding will compute a threshold level wh e r eb y
no Gaussian noise will be left in the denoised signal.
However, Donoho’s universal thresholding is able to
provide us an almost noise-free signal, but the important
drawback of using this thresholding algorithm is the
elimination of possibly informative parts of the signal.
In the EEG signal analysis, it is important that not to
lose potentially useful information during the diagnosis.
Moreover, EEG informative signals often have small am-
plitude. Therefore, high thresholding algorithm is not ap-
propriate for denoising the EEG signal.
On the other hands, SURE denoising (Stein Unbiased
Risk Estimator) and Minimax methods seem adapted to
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R. S. Tung, W. Y. Leong / J. Biomedical Science and Engineering 6 (2013) 152-164
the EEG signal denoising. This is due to two of the algo-
rithms offering low threshold and thus preserving most
of the informative signal while eliminating less noise.
For the SURE denoising method, the value of the
threshold is computed considering a Gaussian noise hy-
pothesis for which a robust estimation of variance is
made. Besides that, SURE denoising method has an im-
portant property whereby it can adap t itself to the signal.
In simple words, the SURE denoising method threshold
is depending on the signal but not only depend on the
estimated noise.
For the Minimax denoising algorithm, it is used a
fixed threshold chosen to yield minimax performance for
mean square error against an ideal procedure. The mini-
max principle is used in statistics in order to design an
estimator. Since the denoised signal can be assimilated to
the estimator of the unknown regression function, the
minimax estimator is the one that realizes the minimum
of the maximum mean square error.
In order to validate the ICA separation methods [12], the
Index of Separability (IS) is chosen to validate the ICA
separation methods. The index of separability is calcu-
lated from the N × N transfer matrix G between the origi-
nal sources and the estimated sources after the ICA
GWA (10)
In order to obtain the Index of Separability (IS), it is
required to take the absolute value of elements G and
normalize the lines gi by dividing each element with the
maximum absolute value of the line. As the result, the
lines of the resulting matrix G will be
The index of separability is obtained by
IS 1
 (12)
For the perfect source separation, the index of separa-
bility is equal zero. (IS = 0) [12].
Besides using the Index of Sep arability (IS) to valid ate
the proper ICA algorithms for processing the EEG sig-
nals, performance index of Signal to Interference Ratio
(SIR) for the mixing matrix A and the signal S is chosen
to be our evaluation criteria as well.
For the performance index of SIR for the mixing ma-
trix A, a problem of one component estimation can be
viewed as the following:
 
iiii ij
where yi and sj are estimated component and the j-th
source respectively, is represent a row vector of
demixing matrix and the gi is a normalized row vector [0
0 gij 0 0]. As the yi is the estimation of sj, the ideal nor-
malized vector gi is the unit vector of
0 010
U .
Therefore, one analysis is successful if and only if its
vector gi is similar to unit vector uj.
For the performance index of SIR for the signal S,
each pair of signal (yi, sj) is then defined as [12]
10log10 ij
To select the most appropriate ICA algorithms for proc-
essing the EEG signal, the simulated signals are gener-
ated for testing the ICA algorithms and compared the
result with known reference sources. Five simulated
sources are created which having frequencies closing to
the real brain signals (sampling frequency = 256 Hz).
The simulated sources are then mixed using random
mixing type in order to create a real-like human EEG
signal as shown in the Figure 3.
To select the appropriate ICA algorithms for separat-
ing the EEG signals, three types of tests have been car-
ried out.
1) The five simulated EEG signals (Figure 1) were
processed directly without add itio n al noise to the mixtur e.
The purpose of this step was to decide a source separa-
tion algorithm in an ideal condition. Thirteen of ICA
algorithms were tested under no noise condition and the
results are shown in Table 1.
From the result in Table 1, Index of Separability (IS)
versus ICA algorithms was plotted in Figure 4. From the
Table 1 and Figure 4, the robust SOBI (SOBI-RO) al-
gorithm will be selected to separate the EEG signal with
the index of separability 0.0700. When the IS approach-
ing to zero, the separation of the signal into independent
components will be better. Besides that, the results also
convince that the second order statistic ICA algorithm
perform well on non-stationary EEG signals.
2) To better approximate the real EEG signals, differ-
ent types of noise (Gaussian and Uniform noise) were
added to the mixtures. As we all know that, the EEG
signal not only consist of brain activities, but it also co n-
tains non-brain activities as well. Therefore, by adding in
different types of noise which range from 20 dB to 0 dB,
the approximation on the ICA algorithms can then be
improved. Thirteen ICA algorithms were tested with
different types of noise (Gaussian and Uniform noise),
the result for the additional Gaussian noise and Uniform
noise is shown in Tables 2 and 3 respectively.
wX wAS
S (13)
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Copyright © 2013 SciRes.
Figure 3. Simulated sources, simulated EEG (mixed signals).
Using the results in Tables 2 and 3, the graph of ISavg
versus ICA algorithms in the presence of Gaussian and
Uniform noise is plotted in Figures 5 and 6 respectively.
From the plotted graph of ISavg versus ICA algorithms in
the presence of noise (Gaussian or Uniform), the robust
SOBI (SOBI-RO) algorithm appears to be a better algo-
rithm in separating the simulated EEG signals.
3) Finally, Monte Carlo Analysis is used to evaluate
the selected ICA algorithms in order to verify the ro-
bustness of the robust-SOBI (SOBI-RO) algorithm. By
running the ICA algorithms under the Monte Carlo
Analysis, the mean value of Signal to Interference ratio
(SIR) for the mixing matrix, A = H and Source signal, S
can be calculated. The main purpose of using Monte
Carlo Analysis is to compare the performance, robust-
ness and consistency of different ICA algorithms for the
same mixing conditions.
For the evaluation of ICA algorithms under Monte
Carlo Analysis, four ICA algorithms have been selected
which are AMUSE, SOBI, SOBI-RO and EFICA. The
R. S. Tung, W. Y. Leong / J. Biomedical Science and Engineering 6 (2013) 152-164
Table 1. Comparison of ICA algorithms in simulated EEG.
Algorithm IS IO
AMUSE 0.0739 0.3126
Evd 2 0.0850 0.2985
SOBI 0.0900 0.2973
SOBI-RO 0.0700 0.1924
SOBI-BPF 0.0904 0.2817
SONS 0.1768 0.5328
FJADE 0.2585 0.4612
JADE TD 0.1950 0.3149
FPICA 0.1226 0.2642
EFICA 0.1099 0.2463
SANG 0.0787 0.3890
ThinICA 0.1199 0.2661
ERICA 0.1742 0.3063
Figure 4. Graph of IS versus ICA algorithms.
result for mean values of Signal to Interference ratio
(SIR) for mixing matrix A = H and mean values for
Source signal, S are shown in Figures 7 and 8 respec-
From the results (Figures 7 and 8), we can clearly ob-
serve that in each row of ICA algorithms (AMUSE,
SOBI, SOBI-RO and EFICA), it separate the signals
successfully with prior knowledge that no additional
noise is added to the mixtures. For a successful separa-
tion of the signals, the Signal to Interference ratio (SIR)
for matrix of A and S must be greater than 16 dB. The
tested algorithms are able to fulfil the criteria for suc-
cessfully separ a t i o n of signal (>16 dB).
In order to compare the robustness of different ICA
algorithms, Gaussian noise of 20 dB is added into the
mixture and run with the Monte Carlo Analysis. Figure
9 show the comparison result of mean SIR for the Source
signal, S. In the noiseless data wh ich is at the left column
of Figure 9, each row of the algorithms is successfully
and consistently separates the signals. On the right col-
umn of the Figure 9, the data is added with Gaussian
noise of 20 dB and from the histogram generated, we
observe that the SOBI-RO and SOBI algorithms are per-
forming better in separating the noisy signal if compare
to the other two algorithms.
Table 2. Separation of noisy signals (Gaussian noise).
Noise Algorithm20151050Average of IS
Evd 20.15670.23210.28830.35150.33600.2729
JEDE TD0.19720.25440.32910.24730.30510.2666
Table 3. Separation of noisy signals (Uniform noise).
Noise Algorithm20151050Average of IS
Evd 20.15610.26090.27970.28700.35380.2675
JEDE TD0.24050.21920.25230.35200.39430.2916
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R. S. Tung, W. Y. Leong / J. Biomedical Science and Engineering 6 (2013) 152-164 159
Figure 5. Graph of ISavg versus ICA algorithms in the
present of noise (Gaussian noise).
Figure 6. Graph of ISavg versus ICA algorithms
in the present of noise (Uniform noise).
Figure 7. Histogram of SIR for S (sources).
Figure 8. Histogram of SIR for A (mixing signals).
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Figure 9. Comparison of noiseless and noise (20 dB) histogram for S.
Instead of using the histogram of SIR for S (source),
histogram of SIR for A (mixing matrix), shown in Figure
10, give reliable measurement especially in the presence
of additional noise in the signal. In the noiseless data
which is at the left colu mn of Figure 10, the result in the
noiseless signal gives a successful separation of signal in
each row of the algorithms. However, in the right column
of the Figure 10, the additional noise (20 dB) showed
the robustness in respect to noise for the selected algo-
As shown the Figure 11, in the presence of the noise
or artifacts, the mean value for SIR will decrease in re-
spect to the addition al noise. This prove that noisy signal
always pose a problem for the ICA algorithm in separat-
ing and reconstruct the signal.
In order to apply the selected ICA algorithms and the
wavelet denoising algorithms, a real EEG signals were
recorder using 10/20 international system. It is a 20 min-
ute sleep recording of a severe Obstructive Sleep Apnea
Syndrome (OSAS) during NREM and REM sleep. Seven
channels were used to record the EEG signals which are
sampled at 100 Hz. The SOBI-RO algorithm was per-
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R. S. Tung, W. Y. Leong / J. Biomedical Science and Engineering 6 (2013) 152-164 161
formed on four channels (C3, O1, C4 and O2), Figure 12.
The four channels were selected due to the position of
the electrode at the location whereby the onset of the
sleeping happens inside a human brain.
From denoising results obtained, we are able to see
that the wavelet denoising method of Heuristic SURE is
performing better than the Minimax denoising algorithm,
Figures 13-16. This is due to Minimax denoising algo-
rithm tends to eliminate the informative EEG signal
which will cause the loss of EEG signal during the proc-
essing of the signal. The denoising results were magni-
fied with the purpose of evaluating the robustness of the
Figure 10. Comparison of noiseless and noise (20 dB) histogram for A.
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Figure 11. Histogram of SIRs for A (mean value). Top: clean; Bottom: noise (20 dB).
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Figure 12. Independent component without denoising (y1 = C3, y2 = O1, y3 = C4 and y4 = O2) running with
SOBI-RO algorithms.
Figure 13. Wavelet denoising with heuristic SURE and minimax on y1 = C3 channel (Top = heuristic SURE, Bottom = minimax).
Figure 14. Wavelet denoising with heuristic SURE and minimax on y2 = O1 channel (Top = heuristic SURE, Bottom = minimax).
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Copyright © 2013 SciRes.
Figure 15. Wavelet denoising with heuristic SURE and minimax on y3 = C4 channel (Top = heuristic SURE, Bottom = minimax).
Figure 16. Wavelet denoising with heuristic SURE and minimax on y4 = O2 channel (Top = heuristic SURE, Bottom = minimax).
denoising algorithms and from the result we obtained, we
are able to understand the denoising algorithm is more
suitable to process the EEG signal with lower amplitude.
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