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Method to reduce the effect of miagrafic and sensory noise with isolating the isoline on ECG signal

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MATEC Web of Conferences 132, 05017 (2017) DOI: 10.1051/matecconf/201713205017
DTS-2017
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution
License 4.0 (http://creativecommons.org/licenses/by/4.0/).
*
Corresponding author: sea.sea@mail.ru
Method to reduce the effect of miagrafic and sensory noise with
isolating the isoline on ECG signal
Evgeny Semenishchev
1,*
, Dmitry Chernyshov
1
, Ilya Svirin
2
1
Don state Technical University, 344000, Rostov-on-Don, Russian Federation
2
CJSC Nordavind, 117545, Moscow, Russian Federation
Abstract: This paper deals with an approach to the analysis of ECG data, which allows to remove the
noise component, to preserve the peaks characterizing the work of the heart, and to identificate floating
isoline.
1 Introduction
Processes automation is one of the priorities of the
modern world. Constant modernization of equipment
requires large investments, as well as retraining of
personnel, installation works and maintenance of new
systems. In this connection, the most promising direction
is the automation of data processing, which allows to
reduce the number of personnel, and to improve the
overall efficiency of the control system. One of the
leading areas of data analysis is the development of the
digital signals processing theory, based on the analysis
of initial data.
The use of digital signal processing methods has
found wide application [1]:
- in automation and control systems
- in modern antenna systems
- in the study of biomechanical parameters, biometric
data collection systems located directly on the object
under study
- in modern systems of computer vision and
automatic processing of two-dimensional signals
- in economics and sociology in the study of trends;
- in information-measuring systems;
- in computer technology to increase accuracy of
analog-digital transformation
Data, received with ECG, in addition to the useful
information on the propagation of electrical impulses in
the cardiac muscle, contains the noise component, which
has a different source. Analog-digital convertion also
adds random distortions to signal [2].
The main task in the signal processing is the
separation of the useful component and attenuation of
the noise component. In practice, a the mean-square
error minimization criterion or the criterion of mean-
absolute deviation is used to determine the processing
quality. Each of this methods has advantages and
limitations of use depending on the task and a priori
information on the components of the input signal. In
this connection, digital signal processing based on the
objective function of the combined criteria becomes
relevant objective. Of particular interest is the use of
multicriterial methods for processing digital signals, that
are represented by a single implementation with a
limited amount of a priori information about the useful
component function and statistical noise characteristics
[3].
Figure 1 contains an algorithm for obtaining
estimates using multi-criteria signal smoothing methods,
based on minimizing the objective functions:
2
1
2
21
1
2
21
2)(),...,,(
n
k
kkk
n
k
kkn
sssYssss
when
adjusting factor.
When implementing the considered smoothing
methods using machine modeling, in the form of
programs, regions of values of the coefficients were
obtained
44
.
4
01
,
0
. ECG data processing requires
real time analysis. It is done by finding estimates of the
objective function in window
k
, and applying sliding
window
l
for all values of the input signal. Here
k
is
size of the window and
is step of sliding window.
The process of obtaining estimates in a sliding
window is performed by parallel processing of the initial
values of the multicriteria objective function in the
window
k
, with various processing parameters
. The
transition between estimates obtained with different
parameters
is accomplished by the condition:
2
1 12
2
2 12
() () ()
() () ()
k kk
k
k kk
s ss p
s
s ss p




Here
)(
1
k
s
,
)(
2
k
s
are input realization
estimates, received with parameters
MATEC Web of Conferences 132, 05017 (2017) DOI: 10.1051/matecconf/201713205017
DTS-2017
2
)(
1 ош
)(
2 ош
,
p
is a threshold value, determined
experimentally with the RMS deviation of the additive
noise component
2.0
n
and equals
15
,
0
p
[3].
Fig. 1. Algorithm for obtaining estimates using multi-criteria
signal smoothing methods.
The need to solve the isoline detection problem is
due to the requirement to adjust the monitoring system to
locate the report points recorded by the ECG device
within the minimum error range of the analog-to-digital
converter (ADC). To solve the problem of finding the
midline, the algorithm presented in Figure 2 was
developed.
Algorithm is shown on figure 2 and implemented as
follows:
At the first step, the noise component, possibly with
nonuniform distribution law is supressed. It is performed
in order to exclude its influence on the middle line
searching method.
In the second step, the R peak is suppressed using the
R-R processing window.
Fig. 2. Isoline searching algorithm.
At the final stage, parameters
)(
ош
are fixed, and
the entire set is processed. The choice of the filtering
method parameter is done using the results shown in
Figure 3.
Fig. 3. A graph of the choice of the smoothing parameter for
isoline selection method
)(
ош
.
Figure 3. - Example of the ECG isoline detection (1 -
normalized ECG model, 2 - normalized ECG model with
pathology, 3 - isoline).
The processing example shown in figure 3 is
obtained with fixed parameters of the middle line search
algorithm. The parameter of the processing window
k
is equal to the value of the R-R interval, the window step
is fixed and is equal to half the processing window
2
/
k
l
, the filtering parameter
8
, i.e. the priority
of the second summand of the objective function is eight
times larger than the first.
MATEC Web of Conferences 132, 05017 (2017) DOI: 10.1051/matecconf/201713205017
DTS-2017
3
)(
1 ош
)(
2 ош
,
p
is a threshold value, determined
experimentally with the RMS deviation of the additive
noise component
2.0
n
and equals
15
,
0
p
[3].
Fig. 1. Algorithm for obtaining estimates using multi-criteria
signal smoothing methods.
The need to solve the isoline detection problem is
due to the requirement to adjust the monitoring system to
locate the report points recorded by the ECG device
within the minimum error range of the analog-to-digital
converter (ADC). To solve the problem of finding the
midline, the algorithm presented in Figure 2 was
developed.
Algorithm is shown on figure 2 and implemented as
follows:
At the first step, the noise component, possibly with
nonuniform distribution law is supressed. It is performed
in order to exclude its influence on the middle line
searching method.
In the second step, the R peak is suppressed using the
R-R processing window.
Fig. 2. Isoline searching algorithm.
At the final stage, parameters
)(
ош
are fixed, and
the entire set is processed. The choice of the filtering
method parameter is done using the results shown in
Figure 3.
Fig. 3. A graph of the choice of the smoothing parameter for
isoline selection method
)(
ош
.
Figure 3. - Example of the ECG isoline detection (1 -
normalized ECG model, 2 - normalized ECG model with
pathology, 3 - isoline).
The processing example shown in figure 3 is
obtained with fixed parameters of the middle line search
algorithm. The parameter of the processing window
k
is equal to the value of the R-R interval, the window step
is fixed and is equal to half the processing window
2
/
k
l
, the filtering parameter
8
, i.e. the priority
of the second summand of the objective function is eight
times larger than the first.
2 Method of searching pathologies for
ECG analysis
For detect pathologies by analyzing the
electrocardiogram obtained by an automated mobile
system and stored on a mobile device. We will develop a
multi-criteria approach to the preliminary detection.
Diagnosis by the means of the developed mathematical
models of both a useful (ideal) ECG and possible
pathologies.
As the first criteria, we will use the square
measurement of the discrepancy between the developed
mathematical model
kmatkmat
sts
)(
and the
established cardiogram
k
Y
:
2
kkmat
Ys
As the second criteria, we will use a function
representing the normalized correlation coefficient:
2
2
kkkk
kkkk
YYgg
YYgg
where:
k
g
- model o.
Like a third criteria we will use resulting index,
frequency area.
1
0
*_
2
n
i
ikfft
n
j
i
eY
Resulting multi-criteria function will have the form:
1
0
*_
2
22
2
21
,...,
n
i
ikfft
n
j
i
n
k
n
k
n
k
n
k
kkmatn
eY
n
Y
Y
n
g
g
n
Y
Y
n
g
g
Yssss
here:
,
,
- parameters that establish weight for each
of the criteria,
n
- set size,
k
fft
_
- frequency index,
j
- imaginary unit.
Each parameters of the criteria are established during
the preparation phase using the experience of specialists
in ECG analysis.
Figure 4 shows the pathology search algorithm for
ECG analysis.
Start
Searching the intersection
points of zero
Normalization of the
input values
Determining the range of
confidence intervals
Determining intervals and
detection areas
Upload
database
the pathology
Calculation of correlation
coefficients
Calculation of correlation
coefficients
Transition to the
frequency domain
Indicating parameters
calculation
Indicating parameters
calculation
Pathology detection
Pathology detection
Pathology detection Pathology detection
Decision on the
pathology
Saving results
yes
no
End
Fig. 4. Pathology search algorithm for ECG analysis.
The algorithm presented in Figure 4 is implemented
as follows:
In the first step, the areas of intersection in
established points of the cardiogram report with the
isoline in the zones confined to confidence intervals are
searched. At the same time, the input values are
normalized in the range of R-R intervals.
In the next step, we make the determination of 5
peaks: P, Q, R, S, T and segments ST and R-R, the QRS
complex. The determination is made according to the
standard ranges [4] shown in Figure 5
In the third step, we use the ranges defined in the
previous step to select intervals. The values for each
selected range are normalized.
At the fifth step, the correlation coefficients are
calculated for each pathology and for each examination
area. Processing is performed in the sliding window. At
the same time, we perform the transition to the frequency
domain and the calculation of the main central moments
for the normalized indicating parameters. The
calculations of the central points are made using the
analysis of the differential coefficient.
MATEC Web of Conferences 132, 05017 (2017) DOI: 10.1051/matecconf/201713205017
DTS-2017
4
Fig. 5. The main complex of ECG.
On the sixth step the obtained frequency coefficients
are compared with a mathematical model of each of the
pathologies and the excess of a threshold value is
detected. The calculation of the established threshold is
also made by analyzing the divergence of the central
moments and correlation coefficients. Pathology is
considered detected if more than two indicators coincide
and in case of repeated confirmation notification
decision is made. In the case of coincidence of all
criteria for ECG analysis and their coincidence with the
investigated pathology, the patient is notified [5].
3
The implementation of the pathology
search methods for the analysis of
electrocardiograms
The first step is a searching for intersection of the fixed
points of the cardiogram report with a baseline in that
zones, which are limited by confidence intervals. We'll
use a value of two quantization levels as confidence limit
[6]. The device uses 10 bits analog-to-digital convertor
or ADC and the range of standard QRS complex
amplitudes for different areas of data sources should not
exceed 22 mm and 25 mm for adults. This limit specifies
the monitoring interval, which is limited in the range of
5mV. It means that the device indicates the intersection
of the baseline when fixed values exceed the confidence
intervals which are limited by two quantization levels
and it's equal to ±0,02 mV. We will impose restrictions
in the form of derivative of the change in direction for
the obtained values. It will be used the criterion of
exceeding the measurement sequence over the baseline
for more than 3 reports as a simple pike detector. The
restrictions on the excess of three reports are empirical,
they are based on the minimum possible duration of
restriction of the QRS complex. As a rule, this QRS
complex lasts 0,08 seconds. For children under the age
of 5 it lasts 0,09, and for children over 10 years 0,10.
When the QRS complex lasts more than 0,11 for adults,
it is said of pathology and suggests ventricular
hypertrophy or ventricular blockade. We get the
minimum duration of QRS complex, which doesn’t
exceed 500 reports at a sampling frequency of the device
limited to 5 kHz. This article introduced a restriction of
the range of fixed changes, which is equal to 100 reports.
It will be made a decision about the intersection of the
baseline during these reports.
We will search for intervals of consecution of the
pikes R-R according to the following procedure: we will
use the complex approach in which the maximum value
will be determined as the main condition for detecting
the R wave, as secondary and confirming conditions we
will also use the relative time and sequence of
intersection intervals of the baselines corresponding to P
and Q and the following ST pikes, as well as their
relative intervals of consecution. We can see the ECG
duration model at the pic.6. Along with the R-R pikes, it
is also possible to detect the remaining pikes and their
ranges according to the data, which was obtained in the
previous stages.
Fig. 6. The duration model ECG within normal limits.
The input values are normalized in the range of P-P
intervals in the next step. The normalization process
consists of fixing the maximum values at a given interval
and dividing all values by a given value. Normalization
of the values allows not to consider the scaling factor for
the subsequent analysis and detection of pathologies. At
the third stage, we produce the allocation of pike and
segment intervals. We produce normalization of the
values in the area of each obtained intervals. We define
the group of central moments, such as mathematical
expectation:
k
Y
YMv
k
kk
)(
dispersion
2
)()(
kkk
YMYMYD
skewness ratio
3
3
)(
)(
)(
k
kk
ka
YD
YMYM
Y
0,10
0,10
0,08
0,18
0,35
P
Q
R
S
T
MATEC Web of Conferences 132, 05017 (2017) DOI: 10.1051/matecconf/201713205017
DTS-2017
5
Fig. 5. The main complex of ECG.
On the sixth step the obtained frequency coefficients
are compared with a mathematical model of each of the
pathologies and the excess of a threshold value is
detected. The calculation of the established threshold is
also made by analyzing the divergence of the central
moments and correlation coefficients. Pathology is
considered detected if more than two indicators coincide
and in case of repeated confirmation notification
decision is made. In the case of coincidence of all
criteria for ECG analysis and their coincidence with the
investigated pathology, the patient is notified [5].
3
The implementation of the pathology
search methods for the analysis of
electrocardiograms
The first step is a searching for intersection of the fixed
points of the cardiogram report with a baseline in that
zones, which are limited by confidence intervals. We'll
use a value of two quantization levels as confidence limit
[6]. The device uses 10 bits analog-to-digital convertor
or ADC and the range of standard QRS complex
amplitudes for different areas of data sources should not
exceed 22 mm and 25 mm for adults. This limit specifies
the monitoring interval, which is limited in the range of
5mV. It means that the device indicates the intersection
of the baseline when fixed values exceed the confidence
intervals which are limited by two quantization levels
and it's equal to ±0,02 mV. We will impose restrictions
in the form of derivative of the change in direction for
the obtained values. It will be used the criterion of
exceeding the measurement sequence over the baseline
for more than 3 reports as a simple pike detector. The
restrictions on the excess of three reports are empirical,
they are based on the minimum possible duration of
restriction of the QRS complex. As a rule, this QRS
complex lasts 0,08 seconds. For children under the age
of 5 it lasts 0,09, and for children over 10 years 0,10.
When the QRS complex lasts more than 0,11 for adults,
it is said of pathology and suggests ventricular
hypertrophy or ventricular blockade. We get the
minimum duration of QRS complex, which doesn’t
exceed 500 reports at a sampling frequency of the device
limited to 5 kHz. This article introduced a restriction of
the range of fixed changes, which is equal to 100 reports.
It will be made a decision about the intersection of the
baseline during these reports.
We will search for intervals of consecution of the
pikes R-R according to the following procedure: we will
use the complex approach in which the maximum value
will be determined as the main condition for detecting
the R wave, as secondary and confirming conditions we
will also use the relative time and sequence of
intersection intervals of the baselines corresponding to P
and Q and the following ST pikes, as well as their
relative intervals of consecution. We can see the ECG
duration model at the pic.6. Along with the R-R pikes, it
is also possible to detect the remaining pikes and their
ranges according to the data, which was obtained in the
previous stages.
Fig. 6. The duration model ECG within normal limits.
The input values are normalized in the range of P-P
intervals in the next step. The normalization process
consists of fixing the maximum values at a given interval
and dividing all values by a given value. Normalization
of the values allows not to consider the scaling factor for
the subsequent analysis and detection of pathologies. At
the third stage, we produce the allocation of pike and
segment intervals. We produce normalization of the
values in the area of each obtained intervals. We define
the group of central moments, such as mathematical
expectation:
k
Y
YMv
k
kk
)(
dispersion
2
)()(
kkk
YMYMYD
skewness ratio
3
3
)(
)(
)(
k
kk
ka
YD
YMYM
Y
0,10
0,10
0,08
0,18
0,35
P
Q
R
S
T
index of kurtosis
3
)(
)(
)(
4
4
k
kk
ka
YD
YMYM
Y
The calculation is made for each segment defined at
this stage and the pathology specified in the
mathematical model. After that, a comparison is made
for a match in the parameters in the range defined by the
rule
3
. This calculation helps to define solution of the
first criterion of the function.
We should set a research window
d
kn
3
1
for
realization of the second criterion of the function. The
search for correlation coefficients and their comparison
is performed in a sliding window in the range of the
interval P-P.
22
n
Y
Y
n
g
g
n
Y
Y
n
g
g
cor
n
k
n
k
n
k
n
k
pat
when k - elements of observations in the range of the
processing window,
pat
cor
- correlation coefficient for
each pathology.
When the threshold value is exceeded, a decision is
made to detect the pathology, if it is confirmed for more
than 30% of the searches in the processing window.
We’ll make the transition to the frequency area using
discrete Fourier transform for realization of the third
criterion of the function.
1
0
*_
2
_
n
i
ikfft
n
j
ikfft
eYX
Comparison in the frequency area will be made
according to the shape of the envelope of the frequency
coefficients and the central moments calculated for them.
The envelope will be constructed using the method of
least squares, taking into account the criterion
min)(
2
xfY
n
. The function
)
(
x
f
is polynomial
with the size of a polynomial not exceeding the 4th
degree. The degree of the polynomial is bounded by the
fourth order because of the computational complexity of
the calculations of these indicators. In the case of
coincidence of polynomial functions, or their
discrepancy with an inaccuracy that does not exceed the
threshold value, it is decided to confirm the diagnosis.
Confirmation of the diagnosis in the frequency area is
made in case of coincidence of the group of central
moments with the central moments of the mathematical
model of the supposed pathologies.
The diagnosis is made after the analysis of the results
of each the components of the objective function.
4 Conclusion
As a result of the conducted researches the approach to
the analysis of electrocardiograms is received. The
proposed approach makes it possible to eliminate the
noise component while retaining the signal pikes.
According to the analysis of the received data, an
algorithm for finding the diagnosis is proposed.
References
1. Chung, S. H., and R. A. Kennedy, Journal of
neuroscience methods, 71-86 (1991)
2. Veeneman, D., and S. BeMent, IEEE transactions on
acoustics, speech, and signal processing, no.2, 369-
377 (1985)
3. Semenishchev, Evgeny, et al. In Proc. EWDTS, 444-
449 (2016)
4. Stadler, Robert, et al. Patent No. 6115628 A, United
States, A61B5/0452
5. Sameni, Reza, et al. Computers in Cardiology (2005)
6. Vorobyov, Sergiy, and Andrzej Cichocki, Biological
Cybernetics. No. 4, 293-303 (2002)
 
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