Gaussian Noise Filtering from ECG by Wiener Filter and Ensemble Empirical Mode Decomposition.
ABSTRACT Empirical mode decomposition (EMD) is a powerful algorithm that decomposes signals as a set of intrinsic mode function (IMF)
based on the signal complexity. In this study, partial reconstruction of IMF acting as a filter was used for noise reduction
in ECG. An improved algorithm, ensemble EMD (EEMD), was used for the first time to improve the noisefiltering performance,
based on the modemixing reduction between near IMF scales. Both standard ECG templates derived from simulator and Arrhythmia
ECG database were used as ECG signal, while Gaussian white noise was used as noise source. Mean square error (MSE) between
the reconstructed ECG and original ECG was used as the filter performance indicator. FIR Wiener filter was also used to compare
the filtering performance with EEMD. Experimental result showed that EEMD had better noisefiltering performance than EMD
and FIR Wiener filter. The average MSE ratios of EEMD to EMD and FIR Wiener filter were 0.71 and 0.61, respectively. Thus,
this study investigated an ECG noisefiltering procedure based on EEMD. Also, the optimal added noise power and trial number
for EEMD was also examined.

Conference Paper: A geometric approach to a non stationary process
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ABSTRACT: In this work, we consider a non stationary random process as a geometric space with a variable curvature. The latter can be, obviously, locally constant leading to a constant local metric tensor or equivalently, a constant autocorrelation for the same interval and hence a local stationary behaviour. As an application to clarify this point view, we have, therefore, used this local curvature approximation for modeling or compressing the image of V2O5/TeO2 amorphous thin film structure with a Gaussian stationary ergodic random process.Proceedings of the 2nd international conference on Mathematical Models for Engineering Science, and proceedings of the 2nd international conference on Development, Energy, Environment, Economics, and proceedings of the 2nd international conference on Communication and Management in Technological Innovation and Academic Globalization; 12/2011  SourceAvailable from: Ahmet Mert
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ABSTRACT: Empirical mode decomposition (EMD) is a recently introduced decomposition method for nonstationary time series. The sum of the decomposed intrinsic mode functions (IMF) can be used to reconstruct the original signal. However, if the signal is corrupted by wideband additive noise, several IMFs may contain mostly noise components. Hence, it is a challenging study to determine which IMFs have informative oscillations or information free noise components. In this study, hierarchical clustering based on instantaneous frequencies (IF) of the IMFs obtained by the HilbertHuang Transform (HHT) is used to denoise the signal. Mean value of Euclidean distance similarity matrix is used as the threshold to determine the noisy components. The proposed method is tested on EEG signals corrupted by white Gaussian noise to show the denoising performance of the proposed method.EUSIPCO 2013; 09/2013 
Conference Paper: A geometric approach to the linear modelling
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ABSTRACT: Since the real model output is a physical reaction to any excitation (input), it should not be modified by the way of measuring or observing it. This is an intrinsic behaviour which allows us to consider the inputs as a base of a relative geometric space of observation. Any physical component that is not observed, such as the measurement or the modelling error, is orthogonal to the observation space, and any completely observed component, is entirely within this space. In this geometric approach, we consider a linear modelling as breaking the real model output in the input linear geometric space. To determine the model output contra variant components which represent conventional linear model coefficients, we use the co and contra variant components transformation relation by means of the input space metric tensor. We will apply this, instead of the least mean square (LMS) and the YuleWalker equations, to estimate the autoregressive model coefficients, by breaking its output (the predicted vector) in the input past values space. Furthermore, using the intrinsic property mentioned above, we have broken the predicted vector in a space with one more orthogonal dimension to the input space in order to be able to estimate the autoregressive prediction error variance.Proceedings of the 5th WSEAS international conference on Circuits, systems and signals; 07/2011
Page 1
Gaussian Noise Filtering from ECG by Wiener Filter
and Ensemble Empirical Mode Decomposition
KangMing Chang & ShingHong Liu
Received: 24 May 2009 /Revised: 13 October 2009 /Accepted: 28 December 2009
# 2010 Springer Science+Business Media, LLC. Manufactured in The United States
Abstract Empirical mode decomposition (EMD) is a
powerful algorithm that decomposes signals as a set of
intrinsic mode function (IMF) based on the signal com
plexity. In this study, partial reconstruction of IMF acting as
a filter was used for noise reduction in ECG. An improved
algorithm, ensemble EMD (EEMD), was used for the first
time to improve the noisefiltering performance, based on
the modemixing reduction between near IMF scales. Both
standard ECG templates derived from simulator and
Arrhythmia ECG database were used as ECG signal, while
Gaussian white noise was used as noise source. Mean
square error (MSE) between the reconstructed ECG and
original ECG was used as the filter performance indicator.
FIR Wiener filter was also used to compare the filtering
performance with EEMD. Experimental result showed that
EEMD had better noisefiltering performance than EMD
and FIR Wiener filter. The average MSE ratios of EEMD to
EMD and FIR Wiener filter were 0.71 and 0.61, respec
tively. Thus, this study investigated an ECG noisefiltering
procedure based on EEMD. Also, the optimal added noise
power and trial number for EEMD was also examined.
Keywords ECG.Gaussiannoise.Wienerfilter.
Ensembleempiricalmode decomposition
1 Introduction
ECG is a vital sign monitoring measurement of heart
activity. During ECG measurement, there may be various
noises, such as muscle contraction, baselines wander, and
powerline interferences, which interfered with the ECG
information identification. Therefore, ECG noise reduction
is an important issue and widely studied for many years
[1–3]. Traditional noise reduction method is based on
standard filter processing, either by lowpass filter or high
pass filter. A lowpass filter was designed to remove high
frequency noise, while a highpass filter was designed to
remove lowfrequency vibration, such as baseline wander
and respiration interference. Although there were numerous
advanced signal processing methods applied on the studies
of ECG noise reduction, such as wavelet [4, 5], adaptive
filter [6], and independent component analysis [7], it is still
an interesting and attractive approach to investigate the
ECG filtering characteristics based on partial reconstruction
of intrinsic mode function (IMF). IMF is an intermediate
product of empirical mode decomposition (EMD), a pre
processing algorithm of Hilbert–Huang transforms (HHTs).
HHT was introduced by Huang [8], which is a general
signal analysis technique and has been widely used in many
fields in recent years. There are two steps involved in HHT.
The first step involves the EMD to extract IMF. The second
step is the Hilbert transform of the decomposed IMF to
obtain timefrequency distribution. EMD is based on the
iterative computation of maximum extreme and minimum
extreme function. The residual signal, called IMF, is
extracted after EMD.
The EMD is adaptive and signaldependent. This
property is valuable for biomedical signal investigation
and can be widely used. For example, dynamic behavior
of atrial fibrillation from surface ECG was studied by
K.M. Chang (*)
Asia University,
Taichung, Taiwan, Republic of China
email: changkm@asia.edu.tw
S.H. Liu
Department of Computer Science and Information Engineering,
Chaoyang University of Technology,
Taichung, Taiwan, Republic of China
J Sign Process Syst
DOI 10.1007/s112650090447z
Page 2
Huang [9]. BlancoVelasco developed an EMDbased
algorithm to remove the baseline wander and high
frequency noise of ECG [10]. Nimunkar and Tompkin
added a pseudohighfrequency noise to IMF, as an aid to
remove powerline noise on ECG. They also developed
complete ECG signalprocessing procedures, such as R
peak detection and feature extraction, based on HHT
approaches [11].
Ensemble EMD (EEMD) is an improved algorithm of
EMD, to reduce the modemixing effect between the next
to IMF scales. The principle of EEMD is to add additional
white noise into the signal with many trials. Noise in each
trial is different, and the added noise can be cancelled out
on an average, if the trial number is high enough. Thus, the
existing part is the signal, as more and more trials are added
in the ensemble [12].
In this study, an interesting ECGfiltering approach
was developed based on the low IMF scales contain
high frequency parts and conversely, and partial recon
struction without lowscale IMF removes high frequency
noise. Thus, the decomposed IMF behaves as the filter
bank. Besides, the lowpass filter performance for ECG
with EMD and EEMD was the major concern in this
study.
Wiener filter is another noisefiltering approach used
in this study. Wiener filter is a welldeveloped and
popular class of optimal filters, which uses the signal
and noise characteristics that are available [13]. Wiener
filter theory is based on the minimization of difference
between the filtered output and desired output. Least
mean square method was used to adjust the filter
coefficients to reduce the square of the difference between
the desired and the actual signal after filtering. There are
many studies on Wiener filter application on biomedical
signal analysis, such as on stress ECG [14], time
frequency ECG representation, and filtering [15]. In this
study, the FIR Wiener filter was adopted to compare
EEMD filter performances. Gaussian white noise was
used as a general frequency noise source and was added
to the clean ECG signal.
The structure of this study is organized as follows:
Section 1 presents the introduction, Section 2 provides the
method description, Section 3 describes the result, while
Sections 4 and 5 present the discussion and conclusion,
respectively.
2 Method
2.1 ECG and Gaussian Noises Preparation
There were two ECG groups used in this study, one was the
standard ECG template derived from ECG simulator; the
other group was from the Arrhythmia ECG database in
MIT/BIH database. The standard ECG template used in this
study was prepared from ECG simulator, type number PS
2210 Patient Simulator, with sampling frequency of
360 Hz, down sampled from 1,000 Hz, duration of 180 s,
preset heart rate of 80 BPM, and online lowpass filter of
0–35 Hz. The standard ECG template was noise free,
without baseline drift and high frequency noise, and was
marked as x(t) in this study. Figure 1 (top) illustrates the
typical standard ECG template segments.
The second ECG group was the real ECG signal derived
from the Arrhythmia ECG database in MITBIH [16].
Sixteen subjects in this database were randomly chosen,
each data containing 30 min durations, with sampling
frequency of 360 Hz.
Gaussian white noise was used as the noise source
and embedded in the ECG signal. In this study, the
Gaussian noise signal was generated by Matlab code
awgn.m, denoted as n(t), with the determined signalto
noise ratio (SNR) ranging from 2 to 18 dB, with the step
of 2 dB. The SNR value greater than 18 dB was not
included in this study, because the signal was rather
“clean” when the SNR was greater than 18 dB. Higher
SNR showed less noise part embedded and a “cleaner”
ECG signal. The contaminated ECG segment with SNR
values of 2 dB and 10 dB are illustrated in Fig. 1 (middle
and bottom), respectively.
The contaminated ECG was denoted as x1(t), and x1(t)=
x(t)+n(t). The noise assessed by SNR was defined as follows:
SNR ¼
PL?1
t¼0x2ðtÞ
PL?1
t¼0n2ðtÞ
ð1Þ
where L is the length of the signal.
2.2 FIR Wiener Filter
The Wiener filter was derived from assuming minimum
mean square error (MMSE) when both the statistical
properties of the signal and noise were known. It comprised
the ratio of cross correlation of the desired signal and noise
to the auto correlation of noise signal. In this study, the FIR
type was adopted, and the formula of the Wiener filter is
given as [13]:
w ¼ R?1
X1X1RX1X
ð2Þ
Where w is the FIR Wiener filter coefficients, and the
cross correlation of x1(t) and x(t),RX1X, autocorrelation of
x1(t), RX1X1were estimated. The x1(t) and x(t), represent
the input signal and desired signal corresponding to x1(t)
and x(t) introduced in the earlier section, respectively.
Wiener filter is especially useful when the power
J Sign Process Syst
Page 3
spectrums of input signal and noise overlap and are not
separable by tradition lowpass filter [13]. In this study,
the FIR Wiener filter was derived from Matlab function
firwiener.m, with filter order ranging from 100 to 300.
2.3 EMD Algorithm
The standard EMD algorithm was derived using following
steps [8]:
(1) Identify all the extreme (maxima and minima) peaks
of the signal (DC component of signal was removed
before preprocessing), s(t).
(2) Generate the upper and lower envelope by the cubic
spline interpolation of the extreme peaks developed in
step (1).
(3) Calculate the mean function of the upper and lower
envelope, m(t).
(4) Calculate the difference signal, d(t)=s(t)−m(t).
(5) If d(t) becomes a zeromean process, then the iteration
is stopped and d(t) is considered as the first IMF,
named c1(t); otherwise, go to step (1) and replace s(t)
with d(t).
(6) Calculate the residue signal, r(t)=s(t)−c1(t).
(7) Repeat the procedure from steps (1) to (6) to obtain the
second IMF, named c2(t). To obtain cn(t), continue the
steps (1)–(6) after n iterations. The process is stopped
when the final residual signal, r(t), is obtained as a
monotonic function.
At the end of the procedure, a residue r(t) and a
collection of n IMF were derived and named from c1(t) to
cn(t). Hence, the original signal can be represented as:
sðtÞ ¼
X
n
i¼1
ciðtÞ þ rðtÞ;
ð3Þ
where r(t) is often regarded as cn+1(t).
The low IMF scales were mainly the highfrequency
components of signal, while the high IMF scales were
the lowfrequency components of signal. Thus, an
EMDbased lowpass filter was developed using the
partial reconstruction of the selected IMF scale, which
is given as:
REMDK¼
X
nþ1
i¼k
ciðtÞ;
ð4Þ
When k=1, the REMD1was equivalent to the original
noisecontaminated ECG.
2.4 EEMD Algorithm
The EEMD algorithm is as follows [12]:
(1) Add a whitenoise series, n(t), to the targeted signal, x
(t), in the following description, x1(t)=x(t)+n(t). The
added noise power from 5 to 25 dB was used to
investigate the EEMD performance.
012345678910
−10
0
10
Standard ECG
0123456789 10
−10
0
10
2 dB
012345678910
−10
0
10
Time (unit: second)
10 dB
Figure 1 (Top) Standard ECG template for 10 s duration. (Middle) Contaminated ECG template with SNR 2 dB noise for 10 s duration. (Bottom)
Contaminated ECG template with SNR 10 dB noise for 10 s duration.
J Sign Process Syst
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(2) Decompose the data x1(t) using the EMD algorithm, as
described in Section 2.3.
(3) Repeat Steps (1) and (2) until the preset trial numbers,
each time with different added whitenoise series of the
samepower.ThenewIMFcombination,cij(t) is achieved,
where i is the iteration number and j is the IMF scale.
(4) Estimate the mean (ensemble) of the final IMF of the
decompositions as the desired output.
EEMD cjðtÞ ¼
P
nt
i¼1cijðtÞ
nt
;
ð5Þ
where nt denotes the trial numbers.
Similar to EMD, an EEMDbased partial reconstruction
of ensemble IMF can be defined as:
REEMDK¼
X
nþ1
j¼k
EEMD cjðtÞð6Þ
2.5 ECG Reconstruction Performance Measurement
A mean square error (MSE) between filter ECG output and
clean ECG was used to measure the filter performance and
can be defined as:
PL?1
where x(t) is one of the clean ECG groups, either standard
ECG template or Arrhythmia ECG database. x
the filter output by the Wiener filter or the partial IMF
reconstructed ECG by EMD or EEMD. The lower MSE
value represents better filtering performance. The MSE for
Gaussian noise is an average of 10 times repetitions.
MSE ¼
t¼0xðtÞ ?
_xðtÞ½?2
L
;
ð7Þ
_ðtÞ is either
3 Results
3.1 Wiener Filter Characteristics
Figure 2 demonstrated both the FIR Wiener filter spectrum
(order=300) and standard ECG template with 10 dB
Gaussian noise. As expected, the Wiener filter was
performed as a lowpass filter. Besides, the phase of the
FIR Wiener filter was found to obey the linear phase
speculation.
The MSE was used to examine the filtering character
istics of the Wiener filter. Figure 3 shows the MSE with
filter order from 10 to 400 under SNR from 2 to 18 dB with
standard ECG template. The MSE value decreased both
when the signal SNR value and the FIR Wiener filter order
increased. As the Wiener filter order increased, the MSE
decreased and finally achieved a “steadystate”. The
“steadystate” Wiener filter order for standard ECG
template was 300, while the filter order was around 100
for Arrhythmia ECG database.
Figure 4 presents Wiener filtered ECG for standard ECG
template. It is obvious that the Gaussian noise is signifi
cantly reduced after Wiener filter processing. There is also
no phase delay for filtered ECG with careful examination
on Rwave location, due to the linear phase property of FIR
Wiener filter.
050 100
Hz
150 200
0
50
100
150
200
250
300
Figure 2 Power spectrum of Wiener filter (filter order=300, solid
line), SNR 10 dB Gaussian noise contaminated standard ECG
template (dash line).
0 100 200300 400
0
0.5
1
1.5
filter order
MSE
2 dB
6 dB
10 dB
14 dB
18 dB
Figure 3 MSE of standard ECG template with FIR Wiener filter. The
xaxis is filter order, and yaxis is MSE value. SNR value of 2 dB
(solid line), 6 dB (diamond), 10 dB (dot line), 14 dB (star) and 18 dB
(circle) are also illustrated.
J Sign Process Syst
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3.2 EMD Decomposition of Standard ECG Template
The EMDderived IMF distributions of standard ECG
template without/with Gaussian noise are shown in Figs. 5
and 6, respectively. As expected from EMD algorithm, the
IMF components were extracted according to the signal
complexity, such as a filter bank that filters out simple
waveform from highfrequency component. Thus, the noise
components were filtered in the lower IMF scale. The QRS
complex of standard ECG template was distributed widely
from scale 1 to 2, as shown in Fig. 5. The first three and the
first two IMF scales of ECG with 2 and 10dB Gaussian
noise, were mainly noise, as shown in Fig. 6a and b,
respectively. The QRS component was distributed in the
middle scales of the IMF. Furthermore, the fourth IMF
scale in Fig. 6a and the third IMF scale in Fig. 6b both
contained QRS component and contaminated Gaussian
noise. This was also called as the “modemixing effect”
between near IMF scales.
3.3 EEMD Decomposition of Standard ECG Template
The corresponding EEMDderived IMF distribution of
Fig. 6 is illustrated in Fig. 7. The improvement of EEMD
with regard to EMD is the modemixing reduction
between the near IMF scales. However, the fourth IMF
scale in Fig. 7a and the third IMF scale in Fig. 7b can be
observed to contain more QRS components and less
Gaussian noise than the same IMF scale given in Fig. 6.
The corresponding IMF spectrum of Figs. 6 and 7 is
shown in Fig. 8, which further demonstrates that EEMD
reduces IMF modemixing between the near IMF scales.
The first two IMF spectrum of EEMD had more
concentrated and localized high frequency spectrum. The
third IMF contained the ECGspectrum component that
ranged below 40 Hz. On the other hand, there was a
significant spectrum overlapping between the IMF scales
at first, second, and third scale on EMD with spectrum
below 40 Hz. Thus, evidently EEMD improved the EMD
modemixing performance and acted as a better filterlike
noise reduction method. With the partial reconstruction of
IMF by removing the low scale with noisecontained IMF,
high frequency noise was removed and a “filtered” clean
ECG was obtained as the output. In the following section,
this concept will be further examined by MSE parameter
to check the reconstructed ECG performance by EMD,
EEMD, and the Wiener filter.
Trial number and added noise power were two influen
tial EEMD factors on the partial IMFreconstruction
performance. Figure 9 shows the MSE of various EEMD
reconstruction scale versus trial numbers. As trial number
increased, the MSE value was significantly decreased, and
reached a saturated state with a slow MSE decrease after
sufficient trialnumber calculations on EEMD. Each partial
reconstruction, REEMDk, obeyed the same trend for k=1 to
13. The larger trial number achieved low MSE value, but it
also required larger computation load. Trial number of 100
was sufficient for the standard ECG template data to
achieve an acceptable MSE performance, compromised
with computation load consideration.
The added noise was the other important EEMD factor,
which represented an extra noise source added to the noise
contaminated signal, and followed with EMD computation.
The ensemble (average) EMD of each IMF was observed to
reduce the mode mixing, and thus, enhanced the separation
of signal and noise. Table 1 lists the MSE of added noise
from 5 to 25 dB. As shown in Table 1, the added noise of
5 dB had the best MSE performance than the other added
noise power. High added noise enhanced the noise
component, and further separated the noise and signal into
distinct IMF scales.
In standard ECG template case, similar MSE perfor
mance was observed for 5 dB and 10 dB added Gaussian
noise with a trial number of 100 (MSE=0.1891 and
MSE=0.1892, respectively). To investigate the optimal
EEMD parameters of trial number and added noise, the
detail information on the last row of Table 1 was examined,
which indicated that the MSE performance ratio of trial
number=500 to trial number=100 were around 1.0405 to
1.0025. This result demonstrated there was only 0.25–
4.05% reduction performance with a trial number=500 than
trial number=100. On the other hand, added noise of 10 dB
had less MSE performance variation than 5 dB added noise
(1.33% vs. 4.05%). From results, 10 dB added noise and a
trial number=00 were chosen as the optimal EEMD
parameters with respect to the absolute MSE and MSE
variation performance.
02468 10
−10
0
10
02468 10
−10
0
10
second
Figure 4 (Top) FIR Wiener filtered (filter order=300) ECG of noisy
standard ECG template (SNR=10 dB) (Bottom).
J Sign Process Syst
Page 6
3.4 ECG Filtering Performance of Wiener Filter, EMD,
and EEMD
The overall MSE performance of standard ECG template
with various SNR is listed in Table 2. The minimum MSE
scales of 2 dB for EMD and EEMD were at REMD4and
REEMD4, respectively, while for the SNR from 4 to 18 dB,
the minimum MSE scale were at REMD3and REEMD3,
respectively. The EEMD had lower MSE than EMD of the
same reconstruction IMF scale. When compared with the
Figure 5 IMF distribution of EMD for standard ECG template (100 times repeats average). From top to bottom is the first IMF scale to 10th IMF
scale. Unit of xaxis is 10 s, and it’s the same unit for Figs. 6, 7, 8 and 9.
J Sign Process Syst
Page 7
FIR Wiener filter, the minimum MSE of EEMD was lower
than that of the FIR Wiener filter within the order 200, but
greater than that of the FIR Wiener filter with order 300, for
SNR from 2 to 18 dB. Thus, the FIR Wiener filter
demonstrated superior noise reduction performance than
EEMD with enough filter order in standard ECG template
case.
The MSE performance of Arrhythmia ECG listed in
Table 3 showed two impressive results. The first result was
the MSE performance of EEMD was superior to EMD and
Figure 6 IMF distribution of EMD for standard ECG template with a SNR 2 dB noise; b 10 dB noise.
J Sign Process Syst
Page 8
to Wiener filter. For all the subjects in Arrhythmia ECG
database, the minimum MSE of EEMD was lower than that
of EMD and FIR Weiner filter. The minimum MSE ratio of
EEMD to EMD was around 0.71±0.06, while the minimum
MSE ratio of EEMD to the FIR Wiener filter (order=10)
was around 0.61±0.09. The MSE of EMD was slightly
lower than that of the FIR Wiener filter (order=10). Also,
the MSE performances of the FIR Wiener filter and EEMD
for Arrhythmia ECG database were different from that for
standard ECG template.
Figure 6 (continued).
J Sign Process Syst
Page 9
Figure 7 IMF distribution of EEMD for standard ECG template with a SNR 2 dB noise; b 10 dB noise.
J Sign Process Syst
Page 10
Figure 7 (continued).
J Sign Process Syst
Page 11
The other impressive result was the minimum MSE
was located mainly at REEMD2and REEMD3. There was
no prior knowledge to estimate which IMF scale
contained the noise component; thus, the partial reduction
of IMF without these IMF scales might achieve a
minimum MSE. Therefore, the only way to determine
the minimum MSE of IMF scale was through trialand
error approach.
Figure 8 IMF power spectrum distribution for standard ECG with 10 dB Gaussian noise by a EEMD; b EMD.
J Sign Process Syst
Page 12
Figure 8 (continued).
J Sign Process Syst
Page 13
Figure 9 Trial number effect of EEMD with partial reconstruction for standard ECG template with 10 dB noise, and 10 dB added noise for
REEMD1(dash line), REEMD2(solid line) and REEMD3(dash line with triangle mark).
Table 1 MSE value of REEMD3 for standard ECG template
(SNR=10 dB) with various added noise under two trial number, 100
and 500, respectively. “Ratio” is the MSE ratio between trial numbers
100 to trial number 500.
added noise (dB)5 10 152025
trial no.=100
trial no.=500
Ratio
0.1891
0.1817
1.0405
0.1892
0.1867
1.0133
0.2010
0.2004
1.0029
0.2213
0.2207
1.0029
0.2430
0.2424
1.0025
SNR2468 1012141618
REMD1
REMD2
REMD3
REMD4
REEMD1
REEMD2
REEMD3
REEMD4
W_100
W_200
W_300
6.741
2.962
1.520
1.284
6.765
2.488
1.201
0.972
1.129
1.095
0.490
4.249
1.870
0.977
1.038
4.337
1.578
0.758
0.783
0.878
0.856
0.346
2.680
1.177
0.627
0.833
2.691
0.974
0.473
0.675
0.666
0.652
0.241
1.688
0.741
0.422
0.806
1.712
0.598
0.296
0.615
0.494
0.483
0.165
1.069
0.469
0.305
0.780
1.068
0.371
0.187
0.584
0.359
0.352
0.113
0.673
0.296
0.249
0.773
0.682
0.233
0.124
0.569
0.255
0.252
0.077
0.425
0.187
0.238
0.795
0.427
0.145
0.087
0.567
0.179
0.177
0.053
0.268
0.118
0.250
0.821
0.273
0.092
0.062
0.561
0.124
0.123
0.036
0.169
0.075
0.270
0.851
0.170
0.057
0.047
0.558
0.085
0.084
0.025
Table 2 MSE value of standard
ECG template with various
SNR noise. Where EMD was
with 100 times computation and
EEMD was with trial num
ber=100 and 10 dB added noise.
W_100 means the FIR Wiener
order with order 100. W_200
and W_300 are with filter order
200 and 300, respectively.
J Sign Process Syst
Page 14
Table 3 MSE value of Arrhythmia ECG by EMD (10 times repeat average), EEMD (trial number=100, 10 dB added noise) and Wiener filter
(order=10 and order=100, denoted as W_10 and W_100, respectively) under SNR=10 dB noise.
Subjects NO. REMD2
REMD3
REMD4
REEMD2
REEMD3
REEMD4
W_10W_100
101
102
103
104
105
106
107
108
109
201
202
203
205
207
208
209
126.9
83.3
189.4
151.6
291.0
245.8
1,303.1
161.9
439.5
67.1
157.1
439.3
72.5
223.6
413.7
140.3
229.7
117.7
596.3
197.5
180.6
375.7
771.7
103.2
237.2
69.7
131.3
279.7
235.2
129.7
361.2
551.7
594.4
204.6
1,391.7
359.7
550.3
1,036.4
962.0
175.8
848.7
215.2
484.0
599.9
505.5
155.1
789.0
1,168.8
97.4
60.0
147.0
109.5
232.4
192.5
1,039.1
128.4
351.2
53.4
125.4
348.7
55.0
178.4
329.8
103.3
148.4
90.1
374.2
152.3
128.1
226.9
574.9
76.9
179.7
38.6
76.3
206.5
155.9
99.9
232.0
364.3
458.0
167.3
1,199.7
288.3
328.0
808.9
679.8
113.8
329.8
159.5
336.5
378.8
439.8
97.5
606.0
1,037.7
141.6
79.4
218.3
136.6
259.6
266.4
1,061.7
131.6
347.7
67.5
152.1
378.3
83.6
165.8
401.0
161.1
140.4
77.7
215.8
136.4
257.6
263.6
1,025.4
126.5
334.1
66.6
150.2
375.6
83.2
163.9
398.6
158.8
IMF scale with minimum MSE for EMD and EEMD was in italics
0123456789 10
−500
0
500
0123456789 10
−500
0
500
012345678910
−500
0
500
0123456789 10
−500
0
500
Time (unit: second)
a
b
c
d
Figure 10 Arrhythmia ECG processing (data 101, 2nd channel) a Raw 101 ECG, b ECG with 10 dB noise, c Wiener filter output of (b) with
filter order=10, and output MSE=141.6, d REEMD2output of (b) with trial number =10 and 10 dB added noise, the output MSE=97.4).
J Sign Process Syst
Page 15
The last two columns of Table 3 showed that the
MSE performance of FIR Wiener filter of order=10 and
order=100 were similar. The FIR Wienerfiltered ECG
and ECG from partial reconstruction of EEMD for
Arrhythmia ECG were shown in Fig. 10. The “filtered”
ECGs by both methods were visibly “clean” when
compared with the original uncontaminated ECG.
4 Discussion
This study was mainly based on the concept the partial
reconstruction of EMDderived IMF to remove noise
similar as a “filter”. EMD is a newly developed algorithm
[17], and can separate signal parts into separate IMF scales
by signal complexity. EMD is also suitable for nonlinear
and nonstationary signals, with adaptive IMF scales.
There is no distinct spectrum range for the fixed IMF
scale; it is a signaldependent method that is neither
similar to traditional filter nor wavelet. This property
offers both advantage as well as disadvantage for EMD
based signal analysis.
When noise was added, EMD collected the high
frequency component in the loworder IMF scale. When
SNR = 2 dB, the noise power was high and the first three
IMF scales were distributed for noise; thus, the QRS
component was found from the fourth IMF. Therefore, the
minimum MSE with 2 dB noise was found at REMD4,
which indicates the deletion of first three IMF scales will
reduce noise. On the other hand, for the other noise power
with SNR from 4 to 18 dB, the noise was distributed in the
first two IMF scales, and therefore, the minimum MSE was
at REMD3.
The main reason for the improved noise reduction
performance by EEMD than EMD was the reduction of
IMF mode mixing. The minimum MSE was found at the
same IMF scale both for EMD and EEMD. Both added
noise and ensemble IMF after computation by trialnumber
time improved separation of signal and noise. With 10 dB
added noise and sufficient trial number, there was an
improved noisefiltering performance by EEMD than EMD,
with the minimum MSE ratio of EEMD to EMD was
around 0.71.
However, unlike the previous study by BlancoVelasco,
we only used the partial reconstruction method, which is
easier and straightforward. BlancoVelasco used a QRS
reserved window filter to extract the QRS component in the
first several IMF [10] that was just owing to the mode
mixing by EMD. However, the EEMD just improved it and
reduced the modemixing effect; therefore, a QRSreserved
window filter was not necessary.
Compared with the minimum MSE value of EEMD and
FIR Wiener filter for Arrhythmia database, the MSE ratio
between EEMD and the Wiener filter was around 0.61,
indicating that EEMD had higher noise reduction perfor
mance than FIR Wiener filter. The Arrhythmia data was the
real ECG data, and this result showed that EEMD had
better performance in the real ECG environment. The FIR
Wiener filter attenuated noise and demonstrated an
“optimal” filtering solution, in terms of minimum MSE
sense. On the other hand, EEMD concentrated the noise
component in the first several IMF scales.
Although EEMD was superior to the FIR Wiener
filter on filtering performance in real ECG signal, the
Wiener filter had lesser computation requirement than
EEMD. For the tradeoff between MSE performance and
computation efficiency, EEMD with trial number 100
and 10 dB added noise was considered as a good
choice. In addition, the Wiener filter order of 300 was
also considered as an acceptable solution for ECG
template.
In the future, the idea of partial IMF reconstruction by
EEMD to remove noise can be widely used and applied to
various biomedical signals, such as respiration, power line
interference, and muscle contraction noise on ECG,
especially when signal and noise is not band restricted. In
the future, with the development of a rule to decide the
selected IMF scale, an ECG noise filtering procedure can
be expected.
5 Conclusion
EEMDbased partial reconstruction with selected added
noise and sufficient trial number is a simple and effective
approach to remove Gaussian noise in ECG. EEMD
improved the previous EMD algorithm, and had a better
performance than FIR Wiener filters, under sufficient trial
number iteration and added noise power.
Acknowledgments
(Taiwan, grant number 982221E468009).
This work was partially supported by NSC
References
1. Sayadi, O., Shamsollahi, M. B. (2008). Modelbased fiducial
points extraction for baseline wandered electrocardiograms.
IEEE Transactions on Biomedical Engineering, 55(1), 347–
351.
2. Salisbury, J. I., Sun, Y. (2007). Rapid screening test for sleep
apnea using a nonlinear and nonstationary signal processing
technique. Medical Engineering and Physics, 29(3), 336–343.
3. Stegle, O., Fallert, S. V., MacKay, D. J., Brage, S. (2008).
Gaussian process robust regression for noisy heart rate data.
IEEE Transactions on Biomedical Engineering, 55(9), 2143–
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