An Improved Total Variation Regularization Method for Denoising Magnetocardiography
The application of magnetocardiography signals to detect cardiac electrical function is a new technology developed in recent years. The magnetocardiography signal is detected with Superconducting Quantum Interference Devices (SQUID) and has considerable advantages over electrocardiography (ECG). It is difficult to extract Magnetocardiography (MCG) signal which is buried in the noise, which is a critical issue to be resolved in cardiac monitoring system and MCG applications. In order to remove the severe background noise, the Total Variation (TV) regularization method is proposed to denoise MCG signal. The approach transforms the denoising problem into a minimization optimization problem and the Majorization-minimization algorithm is applied to iteratively solve the minimization problem. However, traditional TV regularization method tends to cause step effect and lacks constraint adaptability. In this paper, an improved TV regularization method for denoising MCG signal is proposed to improve the denoising precision. The improvement of this method is mainly divided into three parts. First, high-order TV is applied to reduce the step effect, and the corresponding second derivative matrix is used to substitute the first order. Then, the positions of the non-zero elements in the second order derivative matrix are determined based on the peak positions that are detected by the detection window. Finally, adaptive constraint parameters are defined to eliminate noises and preserve signal peak characteristics. Theoretical analysis and experimental results show that this algorithm can effectively improve the output signal-to-noise ratio and has superior performance.
[1] Markku Mäkijärvi, J. Montonen, L. Toivonen, et al. Identification of patients with ventricular tachycardia after myocardial infarction by high-resolution magnetocardiography and electrocardiography. Journal of Electrocardiology, 1993, 26(2):117-24.
[2] J. Farré, M. Shenasa. Medical Education in Electrocardiography. Journal of Electrocardiology, 2017, 50(4):400-401.
[3] L. Lu, K. Yang, X. Kong, R. Yang, Y. Wang. A Real Time, Automatic MCG Signal Quality Evaluation Method Using the Magnetocardiography and Electrocardiography. IEEE Transactions on Applied Superconductivity, 2018:1-1.
[4] F. Shanehsazzadeh, M. Fardmanesh. Low Noise Active Shield for SQUID-Based Magnetocardiography Systems. IEEE Transactions on Applied Superconductivity, 2018, 28(4):1-5.
[5] Bankole. I. Oladapoa, S. Abolfazl Zahedi, Surya C. Chaluvadi, Satya S. Bollapalli, Muhammad Ismail. Model design of a superconducting quantum interference device of magnetic field sensors for magnetocardiography. Biomedical Signal Processing and Control 46 (2018) 116–120.
[6] N. Mariyappa, C. Parasakthi, S. Sengottuvel, et al. Dipole location using SQUID based measurements: Application to magnetocardiography. Physica C: Superconductivity, 2012, 477(none):15-19.
[7] V. Tiporlini, K. Alameh. Optical Magnetometer Employing Adaptive Noise Cancellation for Unshielded Magnetocardiography. Horizon Research Publishing, 2013.
[8] V. S. Poudov. The comparison of possibilities of continuous and discrete wavelet transforms for MCG data processing(C)// International Siberian Workshop on Electron Devices & Materials. IEEE Xplore, 2004.
[9] Y. Dong, H. Shi, J. Luo. Application of Wavelet Transform in MCG-signal Denoising. Mod. Appl. Sci. 2010, 4, 20.
[10] B. Arvinti, A. Isar, R. Stolz, M. Costache. Performance of Fourier versus Wavelet analysis for magnetocardiograms using a SQUID-acquisition system(C)// IEEE International Symposium on Applied Computational Intelligence & Informatics. IEEE, 2011.
[11] N. E. Huang, Z. Shen, S. R. Long, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings A, 1998, 454(1971):903-995.
[12] N. Attoh-Okine, K. Barner, D. Bentil, R. Zhang. The Empirical Mode Decomposition and the Hilbert-Huang Transform. EURASIP Journal on Advances in Signal Processing, 2008, 2008(1):251518.
[13] S. Luo, P. Johnston. A review of electrocardiogram filtering. J Electrocardiol, 2010; 43:486–96.
[14] R. P. Narwaria, S. Verma, P. K. Singhal. Removal of baseline wander and power line interference from ECG Signal – a survey approach. Int J Electr Eng, 2011; 3:107–11.
[15] Z. Wu, N. E. Huang. Ensemble empirical mode decomposition method: A noise-assisted data analysis method. Adv. Adapt. Data Anal. 2009, 1, 1–41.
[16] W. Tong, M. Zhang, Q. Yu. Comparing the applications of EMD and EEMD on time–frequency analysis of seismic signal. J. Appl. Geoph. 2012, 83, 29–34.
[17] K. Dragomiretskiy, D. Zosso. Variational Mode Decomposition. IEEE Trans. Signal Process. 2014, 62, 531–544.
[18] Z. G. Sun, Y. Lei, J. Wang. An ECG signal analysis and prediction method combined with VMD and neural network. In Proceedings of the IEEE International Conference on Electronics Information and Emergency Communication, Macau, China, 21–23 July 2017; pp. 199–202.
[19] L. I. Rudin, S. Osher, E. Fatemi. Nonlinear total variation based noise removal algorithms(C)// Eleventh International Conference of the Center for Nonlinear Studies on Experimental Mathematics: Computational Issues in Nonlinear Science: Computational Issues in Nonlinear Science. Elsevier North-Holland, Inc. 1992.
[20] IvanW Selesnick, Harry L Graber, Douglas S Pfeil, Randall L Barbour. Simultaneous Low-Pass Filtering and Total Variation Denoising. IEEE Transactions on Signal Processing. 2014; 62(5):1109-1124.
[21] S. S. Kumar, N. Mohan, P. Prabaharan, K. P. Soman. Total Variation Denoising Based Approach for R-peak Detection in ECG Signals. Procedia Computer Science, 2016, 93:697-705.
[22] T. Sharma, K. K. Sharma. QRS complex detection in ECG signals using locally adaptive weighted total variation denoising. Computers in Biology and Medicine, 2017, 87:187-199.
[23] A. Chambolle. An algorithm for total variation minimization and applications. J. of Math. Imaging and Vision, 20:89–97, 2004.
[24] P. Rodriguez and B. Wohlberg. Efficient minimization method for a generalized total variation functional. IEEE Trans. Image Process. 18(2):322–332, February 2009.
[25] M. Figueiredo, J. Bioucas-Dias, J. P. Oliveira, and R. D. Nowak. On total-variation denoising: A new majorization-minimization algorithm and an experimental comparison with wavelet denoising. InProc. IEEE Int. Conf. Image Processing, 2006.
[26] Liao, Y.; He, C.; Guo, Q. Denoising of Magnetocardiography Based on Improved Variational Mode Decomposition and Interval Thresholding Method. Symmetry 2018, 10, 269.
[1] Markku Mäkijärvi, J. Montonen, L. Toivonen, et al. Identification of patients with ventricular tachycardia after myocardial infarction by high-resolution magnetocardiography and electrocardiography. Journal of Electrocardiology, 1993, 26(2):117-24.
[2] J. Farré, M. Shenasa. Medical Education in Electrocardiography. Journal of Electrocardiology, 2017, 50(4):400-401.
[3] L. Lu, K. Yang, X. Kong, R. Yang, Y. Wang. A Real Time, Automatic MCG Signal Quality Evaluation Method Using the Magnetocardiography and Electrocardiography. IEEE Transactions on Applied Superconductivity, 2018:1-1.
[4] F. Shanehsazzadeh, M. Fardmanesh. Low Noise Active Shield for SQUID-Based Magnetocardiography Systems. IEEE Transactions on Applied Superconductivity, 2018, 28(4):1-5.
[5] Bankole. I. Oladapoa, S. Abolfazl Zahedi, Surya C. Chaluvadi, Satya S. Bollapalli, Muhammad Ismail. Model design of a superconducting quantum interference device of magnetic field sensors for magnetocardiography. Biomedical Signal Processing and Control 46 (2018) 116–120.
[6] N. Mariyappa, C. Parasakthi, S. Sengottuvel, et al. Dipole location using SQUID based measurements: Application to magnetocardiography. Physica C: Superconductivity, 2012, 477(none):15-19.
[7] V. Tiporlini, K. Alameh. Optical Magnetometer Employing Adaptive Noise Cancellation for Unshielded Magnetocardiography. Horizon Research Publishing, 2013.
[8] V. S. Poudov. The comparison of possibilities of continuous and discrete wavelet transforms for MCG data processing(C)// International Siberian Workshop on Electron Devices & Materials. IEEE Xplore, 2004.
[9] Y. Dong, H. Shi, J. Luo. Application of Wavelet Transform in MCG-signal Denoising. Mod. Appl. Sci. 2010, 4, 20.
[10] B. Arvinti, A. Isar, R. Stolz, M. Costache. Performance of Fourier versus Wavelet analysis for magnetocardiograms using a SQUID-acquisition system(C)// IEEE International Symposium on Applied Computational Intelligence & Informatics. IEEE, 2011.
[11] N. E. Huang, Z. Shen, S. R. Long, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings A, 1998, 454(1971):903-995.
[12] N. Attoh-Okine, K. Barner, D. Bentil, R. Zhang. The Empirical Mode Decomposition and the Hilbert-Huang Transform. EURASIP Journal on Advances in Signal Processing, 2008, 2008(1):251518.
[13] S. Luo, P. Johnston. A review of electrocardiogram filtering. J Electrocardiol, 2010; 43:486–96.
[14] R. P. Narwaria, S. Verma, P. K. Singhal. Removal of baseline wander and power line interference from ECG Signal – a survey approach. Int J Electr Eng, 2011; 3:107–11.
[15] Z. Wu, N. E. Huang. Ensemble empirical mode decomposition method: A noise-assisted data analysis method. Adv. Adapt. Data Anal. 2009, 1, 1–41.
[16] W. Tong, M. Zhang, Q. Yu. Comparing the applications of EMD and EEMD on time–frequency analysis of seismic signal. J. Appl. Geoph. 2012, 83, 29–34.
[17] K. Dragomiretskiy, D. Zosso. Variational Mode Decomposition. IEEE Trans. Signal Process. 2014, 62, 531–544.
[18] Z. G. Sun, Y. Lei, J. Wang. An ECG signal analysis and prediction method combined with VMD and neural network. In Proceedings of the IEEE International Conference on Electronics Information and Emergency Communication, Macau, China, 21–23 July 2017; pp. 199–202.
[19] L. I. Rudin, S. Osher, E. Fatemi. Nonlinear total variation based noise removal algorithms(C)// Eleventh International Conference of the Center for Nonlinear Studies on Experimental Mathematics: Computational Issues in Nonlinear Science: Computational Issues in Nonlinear Science. Elsevier North-Holland, Inc. 1992.
[20] IvanW Selesnick, Harry L Graber, Douglas S Pfeil, Randall L Barbour. Simultaneous Low-Pass Filtering and Total Variation Denoising. IEEE Transactions on Signal Processing. 2014; 62(5):1109-1124.
[21] S. S. Kumar, N. Mohan, P. Prabaharan, K. P. Soman. Total Variation Denoising Based Approach for R-peak Detection in ECG Signals. Procedia Computer Science, 2016, 93:697-705.
[22] T. Sharma, K. K. Sharma. QRS complex detection in ECG signals using locally adaptive weighted total variation denoising. Computers in Biology and Medicine, 2017, 87:187-199.
[23] A. Chambolle. An algorithm for total variation minimization and applications. J. of Math. Imaging and Vision, 20:89–97, 2004.
[24] P. Rodriguez and B. Wohlberg. Efficient minimization method for a generalized total variation functional. IEEE Trans. Image Process. 18(2):322–332, February 2009.
[25] M. Figueiredo, J. Bioucas-Dias, J. P. Oliveira, and R. D. Nowak. On total-variation denoising: A new majorization-minimization algorithm and an experimental comparison with wavelet denoising. InProc. IEEE Int. Conf. Image Processing, 2006.
[26] Liao, Y.; He, C.; Guo, Q. Denoising of Magnetocardiography Based on Improved Variational Mode Decomposition and Interval Thresholding Method. Symmetry 2018, 10, 269.
@article{"International Journal of Electrical, Electronic and Communication Sciences:78921", author = "Yanping Liao and Congcong He and Ruigang Zhao", title = "An Improved Total Variation Regularization Method for Denoising Magnetocardiography", abstract = "The application of magnetocardiography signals to detect cardiac electrical function is a new technology developed in recent years. The magnetocardiography signal is detected with Superconducting Quantum Interference Devices (SQUID) and has considerable advantages over electrocardiography (ECG). It is difficult to extract Magnetocardiography (MCG) signal which is buried in the noise, which is a critical issue to be resolved in cardiac monitoring system and MCG applications. In order to remove the severe background noise, the Total Variation (TV) regularization method is proposed to denoise MCG signal. The approach transforms the denoising problem into a minimization optimization problem and the Majorization-minimization algorithm is applied to iteratively solve the minimization problem. However, traditional TV regularization method tends to cause step effect and lacks constraint adaptability. In this paper, an improved TV regularization method for denoising MCG signal is proposed to improve the denoising precision. The improvement of this method is mainly divided into three parts. First, high-order TV is applied to reduce the step effect, and the corresponding second derivative matrix is used to substitute the first order. Then, the positions of the non-zero elements in the second order derivative matrix are determined based on the peak positions that are detected by the detection window. Finally, adaptive constraint parameters are defined to eliminate noises and preserve signal peak characteristics. Theoretical analysis and experimental results show that this algorithm can effectively improve the output signal-to-noise ratio and has superior performance.", keywords = "Constraint parameters, derivative matrix, magnetocardiography, regular term, total variation. ", volume = "13", number = "6", pages = "432-6", }
