Adaptive Fourier Decomposition Approach to ECG denoising

Presented by Wang, Ze (D-B0-2906-8)

Supervisor: Dr. Wan, Feng

Department of Electrical and Electronics Engineering

Faculty of Science and Technology

10/6/2014

1

Outline2

Introduction Adaptive Fourier Decomposition (AFD) Contributions

Denoising Method Based on the AFD Denoising Technique Judgment – Energy Ratio Implementation

Simulation Results Conclusion and Future Work

Introduction3

GoodProperties

Adaptive Fourier Decomposition4

Mathematical Foundation:

Basis function:

Mono-components:positive phase derivatives

Takenaka-Malmquist system

5

Mathematical Foundation:

RecursiveProcess

Adaptive Fourier Decomposition

6

Example:

Adaptive Fourier Decomposition

Blue: N-th mono-component Red: Combination of first N mono-components

N=2

7

N=5

N=3 N=4

N=6 N=7

72.54% 92.22% 95.66%

99.91%99.73%99.00%

Adaptive Fourier Decomposition

8

Properties: Different decomposition levels

Decomposition level N

Converge fast

Different energy

Energy of mono-components

Adaptive Fourier Decomposition

9

AFD-based denoising method Judgment based on the estimated SNR

Simulations ECG signals

An artificial ECG signal Real ECG signals

Noise Additive Gaussian white noise Muscle and electrode motion Artifacts

Comparison Butterworth low-pass filter Wavelet transform Empirical mode decomposition (EMD) Ensemble empirical mode decomposition (EEMD)

Contributions

Denoising Method Based on the AFD

10

Assumption:

Technique:First several mono-components

Original signal

Denoising Technique of the AFD

11

Noisy artificial signal

12

Red: original signalBlue: reconstructed signal

CombineFirst 2 components

Denoising Technique of the AFD

13

Red: original signalBlue: reconstructed signal

CombineFirst 6 components

Denoising Technique of the AFD

14

Red: original signalBlue: reconstructed signal

CombineFirst 10 components

Denoising Technique of the AFD

15

Red: original signalBlue: reconstructed signal

CombineFirst 18 components

Denoising Technique of the AFD

16

Red: original signalBlue: reconstructed signal

CombineFirst 40 components

Redundancy

Denoising Technique of the AFD

17

Red: original signalBlue: reconstructed signal

CombineFirst 60 components

Redundancy

Denoising Technique of the AFD

18

Red: original signalBlue: reconstructed signal

CombineFirst 80 components

Redundancy

Denoising Technique of the AFD

Judgment – Energy Ratio19

Threshold of the decomposition level = Difficulty

New judgment:

Threshold of the energy ratio:

SNRe: estimated SNR of the noisy signal

20

Energy ratio

Threshold

Relationship

Judgment – Energy Ratio

21

Energy ratio

Threshold

Relationship

Judgment – Energy Ratio

22

Implementation

Threshold

Denoising Steps:1. SNRe → Threshold

23

Threshold

Denoising Steps:1. SNRe → Threshold2. Energy Ratio

Red: original signalBlue: filtered signal

Implementation

24

Threshold

Denoising Steps:1. SNRe → Threshold2. Energy Ratio

Red: original signalBlue: filtered signal

Implementation

25

Threshold

Denoising Steps:1. SNRe → Threshold2. Energy Ratio3. Once

Stop AFD Reconstruct signal

Red: original signalBlue: filtered signal

Implementation

26

Denoising Steps:1. SNRe → Threshold2. Energy Ratio3. Once

Continue → Redundancy

Threshold

Stop AFD Reconstruct signal

Redundancy Red: original signalBlue: filtered signal

Implementation

27

StartN=1

Decompose N-th mono-component

?

N=N+1

FinishReconstruct the original signal by

using first N mono-components

No

YesOld judgment:

decomposition level

Implementation

28

StartN=1

Decompose N-th mono-component

?

N=N+1

FinishReconstruct the original signal by

using first N mono-components

No

YesNew judgment:

energy ratio

Implementation

Simulation Results

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Simulation:real ECG signals + additive Gaussian white noise

30

Real ECG signals from MIT-BIH Arrhythmia

Database

Additive Gaussian white noise

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Denoising AFD Wavelet transform EMD EEMD

Simulation:real ECG signals + additive Gaussian white noise

32

SNR of noisy signals

(dB)

SNR of filtered results (dB)

Wavelet transform with

DB4

Wavelet transform with

DB6AFD

6.8 11.81 11.38 13.35

9.29 13.55 12.87 14.36

12.81 15.84 15.07 17.81

15.83 18.02 17.86 18.36Wavelet transform results: Ercelebi, E., 2004. “Electrocardiogram signals denoising using lifting-based

discrete wavelet transform”. Computers in Biology and Medicine, Vol. 34, No. 6, pp. 479–493.

Simulation:real ECG signals + additive Gaussian white noise

33 Record No.MSE of filtered results

EMD EEMD AFD

101 126.9 97.4 38.24

102 83.3 60.0 51.11

103 189.4 147.0 85.07

104 151.6 109.5 97.03

105 180.6 128.1 79.72

106 245.6 192.5 155.01

107 771.7 574.9 702.14

108 103.2 76.9 33.40

109 237.2 179.7 142.60

201 67.1 38.6 35.33

202 131.3 76.3 34.67

203 279.7 206.5 623.88

205 72.5 55.0 33.95

207 129.7 99.9 59.06

208 361.2 232.0 262.60

209 140.3 103.3 63.10

EMD and EEMD results: Chang, K. M. and Liu, S. H., 2011.

“Gaussian noise filtering from ECG by

wiener filter and ensemble empirical

mode decomposition”. Journal of Signal

Processing Systems, Vol. 64, No. 2, pp.

249–264. SNR of noisy signals:

10dB.

34

Real ECG signals from the MIT-BIH Arrhythmia

Database

Electrode motion artifact from the MIT-BIH Noise

Stress Database

Muscle artifact from the MIT-BIH Noise Stress

Database

Simulation:real ECG signals + muscle and electrode motion artifacts

35

Denoising AFD Butterworth low-pass filter EMD Wavelet transform

Simulation:real ECG signals + muscle and electrode motion artifacts

36

Record No.

SNR of noisy signals = 6dB

SNR of noisy signals = 10dB

SNR of noisy signals = 14dB

SNRemd

SNRbutt

SNRwt

SNRAFD

SNRemd

SNRbutt

SNRwt

SNRAFD

SNRemd

SNRbutt

SNRwt

SNRAFD

100 11.4 5.2 6.1 9.6 14.0 7.3 10.2 13.4 16.8 8.6 14.2 16.4

103 9.9 3.6 6.2 10.3 13.0 4.9 10.2 13.4 15.7 5.6 14.2 16.4

105 9.6 5.5 6.1 10.9 12.0 7.9 10.1 12.8 14.5 9.3 14.1 16.3

119 11.5 6.5 6.1 10.8 14.7 9.6 10.1 14.8 17.3 12.0 14.2 17.8

213 8.9 4.5 6.1 8.0 11.9 10.1 10.1 12.0 14.7 7.0 14.1 14.7

The EMD, Butterworth low-pass filter, wavelet transform results: Blanco-Velasco, M., Weng, B. and Barner, K. E., 2008. “ECG signal denoising and baseline wander correction based on the empirical

mode decomposition”. Computers in Biology and Medicine, Vol. 38, No. 1, pp. 1–13.

Simulation:real ECG signals + muscle and electrode motion artifacts

Conclusion37

AFD-based denoising method Judgment: energy ratio

Simulations ECG signals

An artificial ECG signal Real ECG signals

Noise Additive Gaussian white noise Muscle and electrode motion Artifacts

Comparison Butterworth low-pass filter Wavelet transform Empirical mode decomposition (EMD) Ensemble empirical mode decomposition (EEMD)

AFD

Promising Toolfor ECG

denoising

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Other applications of the AFD Converge fast → Signal and image

compression Mono-components → Non-negative phase

derivatives → Instantaneous frequency

Future Work

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[1] Blanco-Velasco, M., Weng, B. and Barner, K. E., 2008. “ECG signal denoising and baseline wander correction based on the empirical mode decomposition”. Computers in Biology and Medicine, Vol. 38, No. 1, pp. 1–13.

[2] Chang, K. M. and Liu, S. H., 2011. “Gaussian noise filtering from ECG by wiener filter and ensemble empirical mode decomposition”. Journal of Signal Processing Systems, Vol. 64, No. 2, pp. 249–264.

[3] Ercelebi, E., 2004. “Electrocardiogram signals denoising using lifting-based discrete wavelet transform”. Computers in Biology and Medicine, Vol. 34, No. 6, pp. 479–493.

[4] Goldberger, A. L., Amaral, L. A. N., Glass, L., Hausdorff, J. M., Ivanov, P. C., Mark, R. G., Mietus, J. E., Moody, G. B., Peng, C. K. and Stanley, H. E., 2000. “PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals”. Circulation, Vol. 101, No. 23, pp. e215–e220.

[5] McSharry, P. E., Clifford, G. D., Tarassenko, L. and Smith, L. A., 2003. “Adynamical model for generating synthetic electrocardiogram signals”. IEEE Transactions on Biomedical Engineering, Vol. 50, No. 3, pp. 289–294.

[6] Moody, G. B. and Mark, R. G., 2001. “The impact of the MIT-BIH Arrhythmia Database”. IEEE Engineering in Medicine and Biology Magazine, Vol. 20, No. 3, pp. 45–50.

[7] Moody, G. B., Muldrow, W. and Mark, R. G., 1984. “A noise stress test for arrhythmia detectors”. Computers in Cardiology, Vol. 11, No. 3, pp. 381-384.

[8] Qian, T., Wang, Y. B. and Dang, P., 2009. “Adaptive decomposition into mono-components”. Advances in Adaptive Data Analysis, Vol. 1, No. 4, pp. 703–709.

[9] Qian, T., Zhang, L. and Li, Z., 2011. “Algorithm of adaptive Fourier decomposition”. IEEE Transactions on Signal Processing, Vol. 59, No. 12, pp. 5899–5906.

References

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1) Ze Wang, Chi Man Wong, Janir Nuno da Cruz, Feng Wan, Pui-In Mak, Peng Un Mak and Mang I Vai, “Muscle and electrode motion artifacts reduction in ECG using adaptive Fourier decomposition”, the 2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC 2014). Under review.

2) Wei Chen, Ze Wang, Ka Fai Lao and Feng Wan, “Ocular artifact removal from EEG Using ANFIS”, the 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2014). Accepted.

3) Ze Wang, Chi Man Wong, Janir Nuno da Cruz, Feng Wan, Pui-In Mak, Peng Un Mak and Mang I Vai, “Adaptive Fourier decompostion approch for ECG denosing”, Electronics Letters. Submitted.

Publications

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Thank YouQ and A