Adaptive Fourier Decomposition Approach to ECG denoising 1 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

Outline Introduction Denoising Method Based on the AFD 2 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 Introduction Adaptive Fourier Decomposition Good Properties

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

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

Adaptive Fourier Decomposition 6 Adaptive Fourier Decomposition Example:

Blue: N-th mono-component Red: Combination of first N mono-components 7 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

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

Contributions AFD-based denoising method 9 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)

Denoising Method Based on the AFD 10 Denoising Method Based on the AFD

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

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

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

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

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

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

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

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

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

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

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

22 Implementation Denoising Steps: SNRe → Threshold Threshold

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

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

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

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

Implementation Start N=1 ? Old judgment: decomposition level N=N+1 No 27 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

Implementation Start N=1 New judgment: energy ratio N=N+1 No 28 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 Simulation Results

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

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

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

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., 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.

Simulation: real ECG signals + muscle and electrode motion artifacts 34 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

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

Simulation: real ECG signals + muscle and electrode motion artifacts 36 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., 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.

Conclusion AFD Promising Tool for ECG denoising 37 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

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

39 References [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.

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 Thank You Q and A