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2017 8th International Conference on Information Technology (ICIT)
ECG Signal Denoising Using ȕ-Hill Climbing
Algorithm and Wavelet Transform
Zaid Abdi Alkareem Alyasseri 1,2
School of Computer Sciences ,University Science
Malaysia,Pulau Pinang, Malaysia
2
ECE Dept. / Faculty of Engineering, University of
Kufa, Najaf, Iraq
Zaid.alyasseri@uokufa.edu.iq
1
Mohammed Azmi Al-Betar
Department of information technology, Al-Huson
University College,
Al-Huson, Irbid-Jordan
Abstract— Electrocardiogram (ECG) is a graphical recording
of the electrical activity of human heart muscles. ECG is classified
as a non-stationary signal. A major problem encountered with
non-stationary signals is noise removal, particularly when the
signal has a low signal-to-noise ratio (SNR). In this paper, the
authors propose a hybrid method of ȕ-hill climbing combined with
wavelet transform for denoising ECG signals. Selecting wavelet
parameters is a challenging task that is usually performed based
on empirical evidence or experience. Therefore, ȕ-hill climbing
must find the optimal wavelet parameters for ECG signal
denoising that can obtain the minimum mean square error
between the original and the denoised ECG signals. The proposed
method was tested using a standard ECG dataset established by
MIT-BIH. The proposed hybrid method was also evaluated using
two criteria, namely, percentage root mean square difference and
SNR. The proposed method demonstrated outstanding noise
reduction performance for ECG signals, and the quality of the
denoised signal is suitable for clinical diagnosis.
Keywords— ECG ; Signal Denoising ; Wavelet denoising ;
Optimization ; ȕ-Hill Climbing.
I.
INTRODUCTION
Electrocardiogram or (ECG) is a graphical recording of the
electrical activity of human heart muscles. ECG is commonly
used for cardiology tests. ECG recording is conducted by
placing electrodes on the skin for a period of time (depending on
the patient’s condition; the test generally lasts for 10 s) [1]. The
task of the electrodes is to detect any electrical change on the
skin that originates from the heart muscle with each heartbeat
[2]. Thus, ECG signals are classified as non-stationary signals
[2]. A major problem encountered with non-stationary signals is
noise removal, particular when the signal has a low signal-tonoise ratio (SNR). Researchers have proposed various efficient
methods for signal noise reduction. Wavelet transform (WT) is
one of the most widely used approaches for signal processing
[3–7]. It is a powerful tool for representing signals in the time
domain. WT has five parameters, namely, wavelet function
name, decomposition level, thresholding methods, thresholding
selection rule, and threshold rescaling methods. Each of these
parameters has several types or values. TABLE I shows the
978-1-5090-6332-1/17/$31.00 ©2017 IEEE
Ahamad Tajudin Khader
School of Computer Sciences, University Science
Malaysia
Pulau Pinang, Malaysia
Laith Mohammad Abualigah
School of Computer Sciences, University Science
Malaysia
Pulau Pinang, Malaysia
possible ranges of the wavelet denoising parameters. The
thresholding parameters were applied in WT to obtain a smooth
signal. Donoho [7,8] proposed thresholding in wavelet for 1D
and 2D signals. The proposed methods are very efficient in noise
reduction.
WT is the most effective technique for solving the signal
denoising problem, particularly in biomedical signal processing
where WT has been applied for ECG noise reduction [3, 6, 9].
Several techniques have been proposed for denoising ECG
signals in biological signal processing. Most of the previous
methods adopted Donoho’s universal theory [3, 6, 9–11]. A
popular approach for ECG noise reduction is the shrinkage of
wavelet coefficients. Sayadi et al. [3] proposed a new scheme
named bionic WT (BWT) for ECG noise reduction by the
adaptive thresholding of WT. Novak et al. [12] proposed a
procedure for noise removal that uses a detection algorithm for
different noise levels with wavelet. The authors employed soft
thresholding, wherein the thresholding value is based on the
noise level in each signal decomposing level. Singh et al. [13]
proposed a selection method of mother wavelet basis functions
for ECG noise removal in the wavelet domain.
In this paper, the authors propose the use of the ȕ-hill
climbing algorithm for ECG signal denoising to find the optimal
wavelet parameters that will minimize the mean square error
(MSE) between the original and denoised signals. Selecting the
right combination of wavelet parameters is a challenging task
because no technique has been established for determining the
optimal tuning of wavelet denoising parameters, whose selection
is commonly conducted based on experience or empirical
evidence.
This paper is organized as follows. Section 2 describes WT and
Donoho’s theory. Section 3 presents the ȕ-hill climbing
algorithm. The proposed denoising method is explained in
Section 4. The ȕ-hill climbing experiments and results are
discussed in Section 5. Finally, the conclusion is provided in
Section 6.
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2017 8th International Conference on Information Technology (ICIT)
II. ECG BASED ON WAVELET DENOISING
Noise reduction is one of the most difficult challenges in
signal processing [2]. Many researchers have attempted to solve
this problem by using filtering, thresholding, and others
techniques. Wavelet is one of these techniques [19]. In recent
years, wavelet theory has been used extensively in several
problems, such as signal denoising, compression, and feature
extraction [20]. WT has five parameters: (1) the type of wavelet
basis function Ɏ, (2) the decomposition level L, (3) the
thresholding function ȕ, (4) the threshold selection rules Ȝ, and
(5) the threshold rescaling methods ȡ. Each of these parameters
has several values, as shown in TABLE I. Fig. 1 shows the
proposed design technique for denoising ECG signals.
The task of DWT is to decompose the input signal using
different coefficients levels to correct the high frequency of the
input signal. Matlab provides several methods for signal
decomposition through DWT. In addition, Matlab provides a
signal reconstruction technique by applying an inverse DWT
(iDWT). Fig. 3 shows the wavelet denoising task procedure.
Original Signal
De-noised Signal
Compute
DWT
Apply
Thresholding
Compute
iDWT
Fig 3: The wavelet denoising procedure
Fig 1. proposed design technique for optimization Wavelet.
The optimal parameters were evaluated by an objective function
to minimize the MSE between the original and denoised signals.
The wavelet denoising approach was developed based on the
original ECG signal corrupted with white Gaussian noise
(WGN) estimation. Fig. 2 shows the original and noisy ECG
signals with an input SNR noise of 15.
Fig 2. ECG signal corrupted with SNR noise =15 dB.
III. WAVELET DENOISING PRINCIPLE
WT is a powerful tool for time domain representation; it explains
the signal on the basis of the correlation between the translation
and the dilation of a function called the mother wavelet [14].
WTs can be classified as continuous wavelet transform (CWT)
and discrete wavelet transform (DWT) [18]. In this study,
Donoho’s approach was applied to the DWT. A DWT is defined
[13] as follows:
C ( a, b) = ¦ x ( n ) g j , k ( n )
(1)
As mentioned, WT has five parameters, and each parameter has
different types (TABLE I). The efficiency of noise reduction
relies on the selection of wavelet parameters. As shown in Fig.
3, the wavelet denoising process has three phases. The first
phase is the decomposition of the ECG signal using DWT. This
phase involves selecting the appropriate wavelet basis function
(Ɏ) for use in the ECG signal decomposition task. The second
wavelet parameter, that is, the decomposition level (L), is also
selected in this phase based on the ECG signal and experience.
In the second phase, thresholding is applied. The wavelet
provides two standard types of thresholding functions (ȕ),
namely, hard and soft thresholding [7, 8]. The thresholding type
(soft “s” or hard “h”), selection rules (Ȝ), and rescaling methods
(ȡ) must all be selected. These threshold mechanisms must be
applied because the selection will affect the global denoising
performance. The thresholding value is generally defined based
on the standard deviation (ı ) of the noise amplitude [14].
TABLES II and III provide the different types of parameters for
the thresholding selection rule and rescaling methods. Finally,
the thresholding rules are selected according to Equation (2).
(2)
s ( n ) = x ( n ) + σ e( n )
where x(n) is the original ECG signal, e is the noise, ı is the
amplitude of the noise, and n is the number sampling.
TABLE I.
THE RANGES OF THE WAVELET DENOISING PARAMETERS
Wavelet denoising
parameters
Wavelet function Ɏ
n∈Z
where C(a,b) denotes the wavelet dynamic coefficients, a = 2íj,
b = k2íj, j ‫ א‬N, k ‫ א‬Z; a is the size of the time scale, b is the
translation, x(n) is the input ECG signal, and gj,k(n) =
2j/2g(2jník) is the DWT.
Thresholding function ȕ
Method (Range)
1. Meye (meyr),
2. Morlet (morl),
3. Gaussian (gaus1…gaus8),
4. Symlet (sym1 … sym45),
5. Coiflet (coif1 .. coif5),
6. Daubechies (db1..db45),
7. Biorthogonal (bior1.1 .. bior1.5 & bior2.2 ..
bior2.8 & bior3.1 .. bior3.9).
Soft threshold ‘s’ or Hard threshold ‘h’
Decomposition level L
From (1) to (10)
Thresholding selection
rule Ȝ.
Heursure, Rigsure, Sqtwolog, and
Minimax
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2017 8th International Conference on Information Technology (ICIT)
Wavelet denoising
parameters
Method (Range)
Rescaling approach ȡ
‘one’, ‘sln’,’mln’
TABLE II.
SHOWS FOUR THRESHOLD SELECTION RULES
Thresholding rule
Rule 1: Rigrsure
Rule 2: Sqtwolog
Rule 3: Heursure
Rule 4: Minimaxi
problems than other advanced techniques. In this paper, we use
the ȕ-hill climbing algorithm as an optimization technique to
find the optimal wavelet parameters for ECG signal denoising.
Description
Threshold is selected using the principle of
Stein’s Unbiased Risk Estimate (SURE)
Threshold is selected equal to
sqrt(2 ‫ כ‬log(length(signal)))
Threshold is selected according to mixture
(Rigrsure and Sqtwolog)
Threshold is selected equal to Max(MSE)
TABLE III. SHOW THE WAVELET THRESHOLDING RESCALING
METHODS
Wavelet threshold rescaling
methods (ȡ)
one
rescaling
No scaling
sln
Single level
mln
Multiple level
The wavelet parameters (ȕ, Ȝ, and ȡ) must be separately applied
for each wavelet coefficient (approximation and details) level.
In the last phase, the denoised ECG signal is reconstructed by
iDWT.
IV. ȕ-HILL CLIMBING ALGORITHM
The last development in optimization domain related to meta
heuristics which is categories into: evolutionary algorithm [2226], swarm intelligence [27-28], and trajectory algorithms
[15,21,30]. Hill climbing is a simple trajectory-based method
that can find the local optimal solution. It is an iterative
approach that starts with an arbitrary solution to a problem and
then continues the search trajectory in the problem space to find
a better solution. If the previous step produced a better solution,
an incremental change will continue to find a new solution. This
process is repeated until the solution can no longer be improved.
The problem with hill climbing algorithm is that only uphill
movements are accepted, which leads to getting easily stuck in
the local optima [16]. Several extension methods have been
proposed to overcome this problem. The most recent extension
proposed by Al-Betar in 2016 is called ȕ-hill climbing [15],
wherein a single stochastic operator is used in hill climbing to
strike an efficient balance in both exploration and exploitation
during the search. The proposed operator is called the ȕoperator. The ȕ-hill climbing algorithm was inspired by the
uniform mutation operator of the genetic algorithm. At each
iteration, the search space of the current solution is defined
based on the number of problem parameters. In denoising ECG
signals, we use five parameters. The task of the ȕ operator is to
find a new explorative search space of the current solution. Fig.
4 shows the flowchart of the ȕ-hill climbing algorithm. The
proposed method was tested and evaluated using IEEECEC2005 global optimization functions. According to [15,21],
ȕ-hill climbing showed efficient improvements to the hill
climbing algorithm and achieved better results in many global
Fig. 4 Flowchart of ȕ-hill climbing
V. THE HYBRID Ǻ-HILL CLIMBING AND WAVELET FOR ECG
SIGNAL DENOISING
Proposed procedure for ECG signal denoising has three phases
which are summarized below and Fig. 5 shows the flowchart of
the proposed method:
1. First phase (Inputs): Noisy ECG signal and wavelet
denoising parameters (Ɏ, L, ȕ, Ȝ, and ȡ) are the inputs. We
consider that the original ECG signal (MIT-BIH) was
corrupted by the standard white Gaussian noise with a
SNR input noise ranging from 0 to 30.
2. Second phase (Tuning wavelet parameters using the
ȕ-hill climbing algorithm): In this phase, ȕ-hill
climbing will search the ECG signal space to find the
optimal wavelet parameters that can achieve the
minimum objective function. Several kinds of objective
functions have been proposed for solving the denoising
problem. One such objective function is the MSE, which
was proposed in [3,6]. The MSE is the difference
between the original and the ECG denoised signals over
N samples. The MSE equation is given in Equation (3),
where x(n) denotes the original ECG signal and x̂ (n) is
the denoised ECG signal obtained by tuning the wavelet
parameters using the ȕ-hill climbing algorithm.
MSE =
1 N
[x(n) − xˆ (n)]2
¦
n=1
N
(3)
3. Third phase (ECG denoising based on the optimal wavelet
parameters): The denoising process involves the following
steps:
a- ECG signal decomposition using DWT
b- Thresholding based on the coefficients noise level
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2017 8th International Conference on Information Technology (ICIT)
c- Reconstruction of the denoising signal by iDWT
VI. RESULTS AND DISCUSSION
To test and evaluate the efficiency of the proposed ECG
denoising method, several standard benchmarks were obtained
from MIT-BIH [17]. This database has approximately 48 halfhour ECG recordings. Each ECG record has the following
specifications: signal length is 650,000 samples, sampling rate
is 360 Hz, resolution is 11 bits over a 10 mV range, and bit rate
is 3960 bps. The MIT-BIH database has been freely available
in PhysioNet since February 2005. The MIT-BIH database is a
widely used benchmark for comparing and evaluating the
performance of different noise reduction techniques in the
literature.
As mentioned, parameter selection is typically performed based
on experience or empirical evidence. Therefore, the ȕ-hill
climbing algorithm is suggested as an optimization method for
finding the optimal wavelet ECG denoising parameters.
TABLE IV shows the optimal wavelet parameters selected
using the proposed method.
Original
Signal
Add White Gaussian Noise
to original signal and
initial wavelet parameters
First phase
ȕ -Hill
Climbing
Algorith
Second phase
Optimal Wavelet
Parameters
Third phase
Signal decomposition
using DWT
Results evolution using
SNR and PRD
Apply Threshold
methods
Denoised Signal
Signal reconstruction
using iDWT
End
Fig. 5 Flowchart of the purposed method
i7, RAM 8G, using MATLAB R2014a. The ȕ-hill climbing
parameters were 5000 iterations and ȕ-operator = 0.5. As shown
in Table 2, the MSE decreased with the noise value (the
objective function is to minimize MSE), which started at
0.012564875 when the input noise was zero and continued to
decrease until the best minimum value of 7.26028E-05 was
reached at the input noise of 30. At run time, the wavelet
function obtained different ranges, but Daubechies and Symlets
were selected twice (sym3, syn8, db36, and db43). According
to [6,7,14], Daubechies and Symlets are very concise and
facilitate a perfect and simple reconstruction of the original
signal. The decomposition level was defined according to the
noise level, for which the suitable decomposition level was 7
for a high input noise and 2–4 for a low noise. Even though the
hard thresholding method is the simplest approach, the
selection soft thresholding for all noise inputs was the algorithm
proposed. This is because the hard method occasionally causes
discontinuities in the signals [14]. For the thresholding selection
rule parameter, two options, namely, heursure and rigrsure,
were selected; heursure was selected four times and rigrsure
was selected thrice. Finally, the option ‘sln’ in the
wavelet rescaling approach parameter showed dominance
when selected for all input noise levels.
For evaluation, the noise reduction performance was measured
by two criteria, namely, PRD and SNR. PRD and SNR were
computed according to Equations (4) and (5), respectively.
­° ¦ N [x ( n) − xˆ ( n) ]2 ½°
PRD = 100 * ® n =1 N
¾
2
°¿
°̄ ¦ n =1 [x (n )]
(4)
­° ¦ N [x(n)]2
½°
SNR = 10 log10 ® N n =1
2¾
°̄ ¦n =1 [x(n) − xˆ (n)] °¿
(5)
where x(n) denotes the original ECG signal, ‫ݔ‬ො(n) is the denoised
ECG signal obtained by tuning the wavelet parameters through
the ȕ-hill climbing algorithm, and N is the sampling number.
The proposed ECG denoising method was tested on the MITBIH database for 48 ECG signals [17]. The average values of
SNR and PRD were calculated for the signal before and after
denoising using the proposed method. The evaluation
efficiency of wavelet denoising based on the ȕ-hill climbing
algorithm is presented in Table 4 for the ECG signal with an
input SNR ranging from 0 to 30 dB. Fig 6 shows that a linear
relation exists between the input SNR and the output
SNR, as revealed by the proposed method. In addition, PRD
indicates that the proposed method denoises signals smoothly,
particularly when the ECG signal has low noise. The decrease
in PRD indicates the efficiency of the denoising of the original
ECG signal. Moreover, a high SNR corresponds to low noise.
Finally, the proposed denoising method successfully achieved
a high SNR and a low PRD for the ECG signal.
The results in TABLE IV were obtained by implementing the
ȕ-hill climbing algorithm on LENOVO ideapad 310, intel core
99
2017 8th International Conference on Information Technology (ICIT)
TABLE I.
Input
SNR
Noise
0
5
10
15
20
25
30
THE OPTIMAL WAVELET DENOSING PARAMETERS OBTAINED BY THE Ǻ-HILL CLIMBING ALGORITHM
Best F(x)
Wavelet
Function
Decomposition
Level
Thresholding
Function
Thresholding
Selection Rule
Wavelet Rescaling
Approach
0.012564875
0.005507495
0.002123174
0.000902087
0.00037877
0.000166879
7.26028E-05
sym3
rbio4.4
coif3
bior6.8
sym8
db36
db43
7
5
6
4
4
2
4
Soft 's'
Soft 's'
Soft 's'
Soft 's'
Soft 's'
Soft 's'
Soft 's'
heursure
rigrsure
rigrsure
heursure
rigrsure
heursure
heursure
sln
sln
sln
sln
sln
sln
sln
TABLE II.
Input SNR Noise
THE PERFORMANCE OF DENOISING THE ECG SIGNALS FOR DIFFERENT SNR INPUT
Output SNR(dB)
Improvement SNR (dB)
PRD before denoising
PRD after denoising
0
8.9649
5
10
15
20
25
30
12.6986
16.6867
20.404
24.1728
27.7325
31.3455
8.9649
100
35.6249
7.6986
6.6867
5.404
4.1728
2.7325
1.3455
56.1648
31.6086
17.7839
9.9813
5.6258
3.1632
23.1778
14.6442
9.5455
6.1853
4.1056
2.7085
Fig.6 performance of ȕ-hill climbing for ECG signal denosing
Fig.7 Performance of proposed method for input SNR 10 (dB)
100
2017 8th International Conference on Information Technology (ICIT)
[9]
Figures 7 shows the denoised ECG signal from using the
proposed technique (ij = coif3, ȕ = soft, Ȝ = rigrsure, L = 6, and
ȡ = sln) with an output SNR = 16.6867 dB with an input SNR
= 10 dB
as example.
VII. CONCLUSSION
In this study, a new method was proposed for ECG signal
denoising that is based on ȕ-hill climbing and WT. The
proposed method is a preprocessing procedure for analyzing
and classifying tasks with non-stationary signals, such as the
ECG signal. WT has five parameters, and each parameter has
different types. Selecting the wavelet parameters is a
challenging task because it is usually performed based on
empirical evidence or experience. The task of the ȕ-hill
climbing algorithm is to find the optimal wavelet parameters
that can obtain the minimum MSE between the original and
denoised ECG signals. The proposed method demonstrated
outstanding performance in terms of noise removal in ECG
signals, particularly in ECG signals with high noise. The
proposed methods were tested using the MIT-BIH dataset and
were evaluated using PRD and SNR. The proposed method
achieved a high SNR and a low PRD. Finally, the hybridization
of ȕ-hill climbing and WT for signal denoising exhibited
excellent results according to these two criteria. The authors
intend to apply the proposed technique to more complex
signals, such as the EEG signal, in future works.
ACKNOWLEDGMENT
The first author would like to thanks The University Sains
Malaysia (USM) and The World Academic Science (TWAS) for
supporting his PhD study.
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