1. Adaptive Fourier Decomposition Approach to ECG denoising1
Adaptive Fourier Decomposition Approach to ECG denoising
Presented by Wang, Ze (D-B )
Supervisor: Dr. Wan, Feng
Department of Electrical and Electronics Engineering
Faculty of Science and Technology
10/6/2014

2. Outline Introduction Denoising Method Based on the AFD2
Outline
Introduction
Adaptive Fourier Decomposition (AFD)
Contributions
Denoising Method Based on the AFD
Denoising Technique
Judgment – Energy Ratio
Implementation
Simulation Results
Conclusion and Future Work

3. 3
Introduction
Adaptive Fourier Decomposition
Good
Properties

4. positive phase derivatives4
Adaptive Fourier Decomposition
Mathematical Foundation:
Takenaka-Malmquist system
Basis function:
Mono-components:
positive phase derivatives

5. Adaptive Fourier Decomposition5
Adaptive Fourier Decomposition
Mathematical Foundation:
Recursive
Process

6. Adaptive Fourier Decomposition6
Adaptive Fourier Decomposition
Example:

7. Blue: N-th mono-component Red: Combination of first N mono-components7
Adaptive Fourier Decomposition
N=2
N=3
N=4
72.54%
92.22%
95.66%
N=5
N=6
N=7
99.00%
99.73%
99.91%
Blue: N-th mono-component Red: Combination of first N mono-components

8. Adaptive Fourier Decomposition8
Adaptive Fourier Decomposition
Properties:
Different decomposition levels
Decomposition level N
Converge fast
Different energy
Energy of mono-components

9. Contributions AFD-based denoising method9
Contributions
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)

10. Denoising Method Based on the AFD10
Denoising Method Based on the AFD

11. Noisy artificial signal11
Denoising Technique of the AFD
Assumption:
Technique:
Noisy artificial signal
First several mono-components
Original signal

12. Denoising Technique of the AFD12
Denoising Technique of the AFD
Combine
First 2 components
Red: original signal
Blue: reconstructed signal

13. Denoising Technique of the AFD13
Denoising Technique of the AFD
Combine
First 6 components
Red: original signal
Blue: reconstructed signal

14. Denoising Technique of the AFD14
Denoising Technique of the AFD
Combine
First 10 components
Red: original signal
Blue: reconstructed signal

15. Denoising Technique of the AFD15
Denoising Technique of the AFD
Combine
First 18 components
Red: original signal
Blue: reconstructed signal

16. Denoising Technique of the AFD16
Denoising Technique of the AFD
Redundancy
Combine
First 40 components
Red: original signal
Blue: reconstructed signal

17. Denoising Technique of the AFD17
Denoising Technique of the AFD
Redundancy
Combine
First 60 components
Red: original signal
Blue: reconstructed signal

18. Denoising Technique of the AFD18
Denoising Technique of the AFD
Redundancy
Combine
First 80 components
Red: original signal
Blue: reconstructed signal

19. Judgment – Energy Ratio19
Judgment – Energy Ratio
Threshold of the decomposition level = Difficulty
New judgment:
Threshold of the energy ratio:
SNRe: estimated SNR of the noisy signal

20. Judgment – Energy Ratio20
Judgment – Energy Ratio
Energy ratio
Relationship
Threshold

21. Judgment – Energy Ratio21
Judgment – Energy Ratio
Energy ratio
Relationship
Threshold

22. 22
Implementation
Denoising Steps:
SNRe → Threshold
Threshold

23. Implementation Denoising Steps: SNRe → Threshold Energy Ratio 23
Red: original signal
Blue: filtered signal

24. Implementation Denoising Steps: SNRe → Threshold Energy Ratio 24
Red: original signal
Blue: filtered signal

25. Implementation Denoising Steps: SNRe → Threshold Energy Ratio Once25
Implementation
Denoising Steps:
SNRe → Threshold
Energy Ratio
Once
Threshold
Red: original signal
Blue: filtered signal
Stop AFD
Reconstruct signal

26. Implementation Denoising Steps: SNRe → Threshold Energy Ratio Once26
Implementation
Denoising Steps:
SNRe → Threshold
Energy Ratio
Once
Continue → Redundancy
Threshold
Redundancy
Red: original signal
Blue: filtered signal
Stop AFD
Reconstruct signal

27. Implementation Start N=1 ? Old judgment: decomposition level N=N+1 No27
Implementation
N=N+1 No
Start
N=1
Decompose N-th mono-component ?
Yes
Old judgment:
decomposition level
Finish
Reconstruct the original signal by using first N mono-components

28. Implementation Start N=1 New judgment: energy ratio N=N+1 No28
Implementation
N=N+1 No
Start
N=1
Decompose N-th mono-component ?
Yes
New judgment:
energy ratio
Finish
Reconstruct the original signal by using first N mono-components

29. 29
Simulation Results

30. Simulation: real ECG signals + additive Gaussian white noise 30
Real ECG signals from MIT-BIH Arrhythmia Database
Additive Gaussian white noise

31. Simulation: Denoising AFD Wavelet transform EMD EEMD31
Simulation:
real ECG signals + additive Gaussian white noise
Denoising
AFD
Wavelet transform
EMD
EEMD

32. SNR of filtered results (dB)32
Simulation:
real ECG signals + additive Gaussian white noise
SNR of noisy signals
(dB)
SNR of filtered results (dB)
Wavelet transform with DB4
Wavelet transform with DB6
AFD
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
18.36
Wavelet transform results: Ercelebi, E., “Electrocardiogram signals denoising using lifting-based discrete wavelet transform”. Computers in Biology and Medicine, Vol. 34, No. 6, pp. 479–493.

33. MSE of filtered results
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 33
EMD and EEMD results: Chang, K. M. and Liu, S. H., “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. Simulation: real ECG signals + muscle and electrode motion artifacts34
Simulation:
real ECG signals + muscle and electrode motion artifacts
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

35. Simulation: Denoising AFD Butterworth low-pass filter EMD35
Simulation:
real ECG signals + muscle and electrode motion artifacts
Denoising
AFD
Butterworth low-pass filter
EMD
Wavelet transform

36. Simulation: real ECG signals + muscle and electrode motion artifacts36
Simulation:
real ECG signals + muscle and electrode motion artifacts
Record No.
SNR of noisy signals = 6dB
SNR of noisy signals = 10dB
SNR of noisy signals = 14dB
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
15.7
5.6
105
5.5
10.9
12.0
7.9
10.1
12.8
14.5
9.3
14.1
16.3
119
11.5
6.5
10.8
14.7
14.8
17.3
17.8
213
8.9
4.5
8.0
11.9
7.0
The EMD, Butterworth low-pass filter, wavelet transform results: Blanco-Velasco, M., Weng, B. and Barner, K. E., “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.

37. Conclusion AFD Promising Tool for ECG denoising37
Conclusion
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 Tool
for ECG
denoising

38. Future Work Other applications of the AFD38
Future Work
Other applications of the AFD
Converge fast → Signal and image compression
Mono-components → Non-negative phase derivatives → Instantaneous frequency

39. 39
References
[1]
Blanco-Velasco, M., Weng, B. and Barner, K. E., “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., “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., “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., “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., “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., “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., “A noise stress test for arrhythmia detectors”. Computers in Cardiology, Vol. 11, No. 3, pp
[8]
Qian, T., Wang, Y. B. and Dang, P., “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., “Algorithm of adaptive Fourier decomposition”. IEEE Transactions on Signal Processing, Vol. 59, No. 12, pp. 5899–5906.

40. 40
Publications
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.
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.
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.

41. 41
Thank You
Q and A