Optimum ECG signal filtering based on wavelet transformation

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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.

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Ecg signal, wavelet simlet 8, wavelet coiflets 5, thresholding method, optimal level

Короткий адрес: https://sciup.org/147236497

IDR: 147236497   |   DOI: 10.14529/ctcr210415

Текст краткого сообщения Optimum ECG signal filtering based on wavelet transformation

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 SNR 1 = 35, SNR 2 = 40, SNR 3 = 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.

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.

  • F ig. 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 SNR 1 = 35, SNR 2 = 40, SNR 3 = 45.

  • F ig. 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 SNR 1 = 35, SNR 2 = 40, SNR 3 = 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.

    Parameter combinations

    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.

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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