CC BY
16
DOI: 10.14529/ctcr210415
OPTIMUM ECG SIGNAL FILTERING BASED ON WAVELET TRANSFORMATION
B.B. Saidov1'2, matem.1994@mail.ru, saidovb@susu.ru, V.F. Telezhkin1, telezhkinvf@susu.ru
1 South Ural State University, Chelyabinsk, Russian Federation,
2 Tajik Technical University named after academician M.S. Osimi, Dushanbe, Republic of Tajikistan
The development of digital signal processing and microprocessor technology creates conditions for improving methods for diagnosing the functional state of organs. Wavelet analysis is a modern and promising method of information processing. In order to determine the effective optimal filtering of the electrocardiography signal based on the wavelet transform, wavelet filtering was performed using wavelets of different families, the efficiency of using different levels of decomposition, methods for calculating the threshold and types of the threshold function was investigated. Aim. Determination of effective optimal filtering of electrocardiography signal based on wavelet transform. Materials and methods. Cardiograms were taken for analysis. Then they were digitized and entered into a computer for processing. A program was written in the Matlab environment that implements continuous and discrete wavelet transform. Results. As a result of the research, 56 combinations of noise reduction parameters were tested for three noise levels. It was found that the maximum degree of signal purification from noise was obtained using the Coiflets 5 wavelet using a rigid thresholding method, with a heuristic method for calculating the threshold value. Wavelet Simlet 8 has lower correlation coefficient values than Coiflets 5, at 35 dB the best result is 97%, the noise level is 40 dB the best result is 98.7%, the noise level is 45 dB the best result is 99.3%, which is generally negligible differs from the correlation coefficients of the wavelet Coiflets 5. Conclusion. As a result of the study, the first and the present work, the following conclusions were made: the optimal level of the wavelet decomposition of the ECG signal N = 2; the maximum degree of signal cleaning from noise was obtained using the Coiflets 5 wavelet using a rigid thresholding method, with a heuristic method for calculating the threshold value; Simlet 8 wavelet using a soft thresholding method with a minimax thresholding method also shows noteworthy results, slightly inferior to Coiflets 5 wavelet results.
Keywords: ECG signal, wavelet Simlet 8, wavelet Coiflets 5, thresholding method, optimal level.
Introduction
The development of means of digital signal processing and microprocessor technology create conditions for improving methods for diagnosing the functional state of organs [1-3]. Wavelet analysis is a modern and promising method of information processing. The wavelet analysis apparatus was developed in the early 1980 [4-6]. The results obtained in various fields using wavelet analysis have increased interest in this area and contribute to its continuous development [7-9].
Wavelet analysis can be successfully used to smooth and remove noise in the ECG signal. The cardio signal stripped of noise components, looks clearer, while its volume is from 10% to 5% of the original signal, which largely solves the problem of storing cardiac records [10-12].
To implement the procedure for the wavelet filtering of the CS, the method of threshold processing of the coefficients was chosen. In the course of the work, an algorithm for the wavelet filtering of the CS by the thresholding method was developed and implemented. There is a wide choice of wavelet bases used for filtering signals by the thresholding method, the choice of the wavelet function and noise reduction parameters, such as the type of threshold, the level of decomposition, etc., plays a decisive role in the operation of the method [13-15].
In order to determine the effective optimal filtering of the electrocardiography signal based on the wavelet transform, wavelet filtering was performed using wavelets of different families, the efficiency of using different levels of decomposition, methods for calculating the threshold and types of the threshold function was investigated.
Determination of the effective filter parameters
Let us determine the signal-to-noise ratio and the correlation coefficient for each set of parameters for the selected decomposition level N = 2.
Let's test 7 selected types of wavelet functions: Haar wavelet; Daubechies wavelet 4; Daubechies wavelet 6; Coiflets wavelet 5; wavelet Simlet 4; wavelet Simlet 6; wavelet Simlet 8.
For each type of wavelet, we use a hard or soft thresholding method. Let us calculate the threshold value by each of the four methods for calculating the threshold: adaptive, heuristic, logarithmic and minimax calculation method.
Thus, for the study, it is necessary to enumerate 56 variants of possible combinations of noise reduction parameters for each noise level.
The calculated data are presented in Tables 1, 2, each cell contains data for three noise levels SNRj = 35, SNR2 = 40, SNR3 = 45.
Consider the signal-to-noise ratio for all combinations of parameters; the calculation results are shown in Table 1.
Table 1
Signal-to-noise ratios for all combinations of parameters
Parameters Soft method Hard method
rigrsure sqtwolog minimaxi heursure rigrsure sqtwolog minimaxi heursure
36.740 36.805 36.829 36.880 36.770 36.695 36.697 36.668
Haar 38.150 38.078 38.107 38.15 38.112 38.146 38.092 38.094
38.620 38.619 38.638 38.64 38.634 38.626 38.642 38.621
39.994 39.886 40.166 40.028 39.552 39.881 39.586 39.796
Simlet 4 43.372 42.971 43.47 43.223 43.115 43.258 43.298 43.137
45.246 45.278 45.224 45.276 45.17 45.171 45.306 45.181
39.964 39.716 39.836 39.669 39.614 39.505 39.877 39.673
Simlet 6 42.846 42.950 42.999 43.015 42.811 43.055 43.236 43.002
44.643 44.733 44.755 44.603 44.734 44.657 44.681 44.683
40.512 40.530 40.517 40.440 40.382 40.248 40.48 40.535
Simlet 8 44.033 44.264 43.906 44.23 44.149 43.838 44.054 43.946
46.427 46.535 46.502 46.544 46.613 46.363 46.456 46.458
39.958 40.079 40.058 39.994 39.751 40.273 40.021 40.16
Daubechies 4 43.430 43.400 43.446 43.616 43.273 43.582 43.222 43.237
45.306 45.083 45.320 45.309 45.435 45.268 45.335 45.225
39.619 39.446 39.643 39.804 39.957 40.135 40.039 39.904
Daubechies 6 43.031 42.978 43.194 43.108 43.153 43.005 43.237 42.821
45.057 44.874 44.871 44.937 44.961 44.893 44.934 44.970
40.575 40.102 40.001 40.440 40.525 40.279 40.290 40.770
Coiflets 5 43.865 43.634 44.022 43.764 44.192 44.025 44.236 44.404
46.828 46.975 46.697 46.811 46.832 46.642 46.655 46.863
As a result of the analysis of the obtained data on the signal-to-noise ratios of all combinations of parameters, it was revealed:
- the least effective wavelet for filtering ECG signals is the Haar wavelet;
- the most optimal wavelet from the Simlet family - Simlet 8;
- Daubechies 4 wavelet has a higher signal-to-noise ratio for all noise levels than Daubechies 6 wavelet;
- Simlet 8 and Coiflets 5 wavelets have the highest signal-to-noise ratios among the considered wavelets.
Consider the correlation coefficients for all combinations of parameters, the calculation results are shown in Table 2.
Саидов Б.Б., Тележкин В.Ф.
Оптимальная фильтрация сигнала ЭКГ на основе вейвлет-преобразования
Table 2
Correlation coefficients for all combinations of parameters
Parameters Soft method Hard method
rigrsure sqtwolog minimaxi heursure rigrsure sqtwolog minimaxi heursure
92.4 92.5 92.6 92.5 92.5 92.3 92.4 92.4
Haar 94.5 94.4 94.4 94.5 94.4 94.5 94.4 94.4
95.0 95.0 95.1 95.1 95.1 95 95.1 95
96.5 96.4 96.6 96.6 96.2 96.5 96.2 96.4
Simlet 4 98.4 98.3 98.4 98.4 98.3 98.3 98.4 98.3
98.9 99 98.9 99.0 98.9 98.9 99.0 98.9
96.5 96.4 96.5 96.3 96.3 96.2 96.3 96.3
Simlet 6 98.2 98.2 98.3 98.2 98.2 98.2 98.3 98.3
98.8 98.8 98.8 98.8 98.8 98.8 98.8 98.8
97.0 96.8 97.0 96.9 96.9 96.7 96.9 97
Simlet 8 98.6 98.7 98.6 98.7 98.7 98.5 98.6 98.6
99.2 99.2 99.2 99.2 99.2 99.2 99.2 99.2
96.5 96.6 96.6 96.6 96.3 96.8 96.6 96.7
Daubechies 4 98.4 98.4 98.4 98.5 98.3 98.4 98.3 98.3
99.0 98.9 99.0 99.0 99.0 98.9 99.0 98.9
96.3 96.1 96.3 96.5 96.4 96.7 96.7 96.5
Daubechies 6 98.3 98.2 98.3 98.3 98.3 98.2 98.3 98.1
98.9 98.8 98.8 98.9 98.9 98.9 98.9 98.9
97.0 96.6 96.5 96.9 96.9 96.7 96.8 97.2
Coiflets 5 98.6 98.6 98.6 98.5 98 98.6 98.7 98.7
99.3 99.3 99.2 99.3 99.3 99.2 99.2 99.3
As a result of the analysis of the obtained data on the correlation coefficients for all combinations of parameters, it was revealed:
- filtering using the Haar wavelet showed the worst results;
- the most optimal wavelet from the Simlet family - Simlet 8;
- Daubechies 4 wavelet at all noise levels has better correlation coefficients than Daubechies 6;
- The highest correlation coefficients were obtained as a result of filtering with Simlet 8 and Coiflets 5 wavelets.
After considering and generalizing the conclusions made on the calculated signal-to-noise ratios and correlation coefficients, two wavelets that filter the ECG signal most effectively were identified: Simlet 8 and Coiflets 5.
To visualize the collected data and identify the optimal set of parameters for each of the two identified wavelets, a graphical data analysis program was written. Figs. 1, 2 show the result of the graphical data analysis program.
Fig. 1 shows a comparison of the output signal-to-noise ratios of Simlet 8 and Coiflets 5 wavelets for eight combinations of parameters presented in Table 1. The figure shows three graphs for three noise levels SNR1 = 35, SNR2 = 40, SNR3 = 45.
Fig. 2 shows a comparison of the correlation coefficients of the Simlet 8 and Coiflets 5 wavelets for eight combinations of parameter parameters presented in Table 2. The figure shows three graphs for three noise levels SNR1 = 35, SNR2 = 40, SNR3 = 45.
As a result of the graphical analysis of the collected data, it was revealed:
- The highest output signal-to-noise ratio for all considered noise levels has the Coiflets wavelet 5 using a rigid thresholding method, with a heuristic method for calculating the threshold value;
- for most sets of parameters the values of the signal-to-noise ratio of the wavelet Coiflets 5 exceed the values of the signal-to-noise ratio of the wavelet Simlet 8, which is especially clearly seen for the input noise level of 45 dB;
- The largest values of the correlation coefficient for all considered noise levels (97.2%, 98.7%, 99.3%) have the Coiflets 5 wavelet using a rigid thresholding method, with a heuristic method for calculating the threshold value;
- Simlet 8 wavelet has lower correlation coefficient values than Coiflets 5, at a noise level of 35 dB the best result is 97%, a noise level of 40 dB is the best result 98.7%, a noise level of 45 dB is the best result 99.3%, which, in general, slightly different from the correlation coefficients of the wavelet Coiflets 5;
- Simlet 8 wavelet shows good filtering results using soft thresholding method, with minimax thresholding method.
Fig. 1. Comparison of the output signal-to-noise ratios of Simlet 8 and Coiflets 5 wavelets for eight combinations of parameters
Fig. 2. Comparison of the correlation coefficients of wavelets Simlet 8 and Coiflets 5 for eight combinations of parameters
As a result of the research, 56 combinations of noise reduction parameters were tested for three noise levels. It was found that the maximum degree of signal purification from noise was obtained using the Coiflets 5 wavelet using a rigid thresholding method, with a heuristic method for calculating the threshold value.
Саидов Б.Б., Тележкин В.Ф.
Оптимальная фильтрация сигнала ЭКГ на основе вейвлет-преобразования
Conclusion
As a result of the study, the following conclusions were made: optimal level of wavelet decomposition of ECG signal N = 2; the maximum degree of signal purification from noise was obtained using Coiflets 5 wavelet using a rigid thresholding method, with a heuristic method for calculating the threshold value; Simlet 8 wavelet using a soft thresholding method, with a minimax thresholding method, also shows noteworthy results, slightly inferior to the Coiflets 5 wavelet results.
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Received 10 March 2021
УДК 53.08
DOI: 10.14529/ctcr210415
ОПТИМАЛЬНАЯ ФИЛЬТРАЦИЯ СИГНАЛА ЭКГ НА ОСНОВЕ ВЕЙВЛЕТ-ПРЕОБРАЗОВАНИЯ
Б.Б. Саидов1'2, В.Ф. Тележкин1
1 Южно-Уральский государственный университет, г. Челябинск, Россия,
2 Таджикский технический университет имени академика М. С. Осими, г. Душанбе, Республика Таджикистан
Развитие средств цифровой обработки сигналов и микропроцессорной техники создают условия для совершенствования методов диагностики функционального состояния органов. Вейвлетный анализ - это современный и перспективный метод обработки информации. С целью определения эффективных оптимальных фильтраций сигнала электрокардиографии на основе вейвлет-преобразования в работе была произведена вейвлет-фильтрация с использованием вейвлетов разных семейств, исследована эффективность применения различных уровней разложения, способов расчета порога и видов пороговой функции. Цель исследования: определение эффективных оптимальных фильтраций сигнала электрокардиографии на основе вейв-лет-преобразования. Материалы и методы. Для анализа были взяты кардиограммы. Далее они были оцифрованы и введены в компьютер для обработки. Была написана программа в среде МА^АВ, реализующая непрерывное и дискретное вейвлет-преобразование. Результаты. В результате исследования были протестированы 56 комбинаций параметров шумоподавления для трех уровней шума. Было выявлено, что максимальная степень очистки сигнала от шума была получена с использованием вейвлета Койфлета 5 с использованием жесткого метода пороговой обработки, с эвристическим способом расчета порогового значения. Вейвлет Симмлета 8 имеет меньшие значения коэффициента корреляции, чем Койфлет 5, на уровне шума 35 дБ наилучший результат 97 %, на уровне шума 40 дБ наилучший результат 98,7 %, на уровне шума 45 дБ наилучший результат 99,3 %, что в целом незначительно отличается от коэффициентов корреляции вейвлет Койфлета 5. Заключение. В результате исследования были сделаны следующие выводы: оптимальный уровень вейвлет разложения ЭКГ сигнала N = 2; максимальная степень очистки сигнала от шума была получена с использованием вейвлет Койфлета 5 с использованием жесткого метода пороговой обработки, с эвристическим способом расчета порогового значения; вейвлет Симмлета 8 с использованием мягкого метода пороговой обработки, с минимаксным способом расчета порогового значения также показывает достойные упоминания результаты, незначительно уступающие результатам вейвлета Койфлета 5.
Ключевые слова: ЭКГ сигнал, вейвлет Симмлета 8, вейвлет Койфлета 5, метод пороговой обработки, оптимальный уровень.
Саидов Бехруз Бадридинович, инженер-исследователь, аспирант кафедры инфокоммуни-кационных технологий, Южно-Уральский государственный университет, г. Челябинск; Таджикский технический университет имени академика М.С. Осими, г. Душанбе, Республика Таджикистан; matem.1994@mail.ru, saidovb@susu.ru.
Тележкин Владимир Федорович, д-р техн. наук, профессор кафедры инфокоммуникационных технологий, Южно-Уральский государственный университет, г. Челябинск; telezhkinvf@susu.ru.
Поступила в редакцию 10 марта 2021 г.
ОБРАЗЕЦ ЦИТИРОВАНИЯ
FOR CITATION
Saidov, B.B. Optimum ECG Signal Filtering Based on Wavelet Transformation / B.B. Saidov, V.F. Telezhkin // Вестник ЮУрГУ. Серия «Компьютерные технологии, управление, радиоэлектроника». - 2021. - Т. 21, № 4. -С. 167-172. DOI: 10.14529/ctcr210415
Saidov B.B., Telezhkin V.F. Optimum ECG Signal Filtering Based on Wavelet Transformation. Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control, Radio Electronics, 2021, vol. 21, no. 4, pp. 167-172. DOI: 10.14529/ctcr210415
