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Revista de Matemática Teoría y Aplicaciones
versão impressa ISSN 1409-2433
Rev. Mat vol.21 no.2 San José Jul./Dez. 2014
Filtros no lineales para reconstruir señales de electrocardiogramas
Nonlinear filters to reconstruct electrocardiogram signals
Nonlinear filters to reconstruct electrocardiogram signals
Resumen
Las señales de los electrocardiogramas han sido usadas en patologías cardíacas para detectar enfermedades del corazón. El objetivo principal de este trabajo es proponer técnicas de filtraje de señales para reducir el ruido, extraer información, reconstruir los estados, y propiedades morfológicas de los latidos del corazón. Adicionalmente se pretende representar la actividad cardíaca en forma simple, informativa, precisa, y de fácil interpretación para los Cardiólogos. Para lograr estos objetivos se proponen implementar los siguientes algoritmos: filtro de partículas genérico (FPG), filtro de partículas con remuestreo (FPR), filtro de Kalman sin esencia (FKSE), y el filtro de partículas sin esencia (FPSE), considerando la estructura básica del modelo dinámico sintético de McSharry et al. (2003) [16]. Los resultados demuestran que los filtros se desempeñan muy bien en la reconstrucción de los estados del sistema del ritmo cardíaco, aun introduciendo pequeñas variaciones en las varianzas de los ruidos de la ecuación de observación; es decir, losmétodos tiene la capacidad de reproducir la señal original del modelo sintético simulado y del modelo sintético con datos reales en forma precisa. Finalmente se evalúa el desempeño de los filtros en términos de la desviación estándar empírica, observándose poca variabilidad entre los errores estimados y una rápida ejecución de los algoritmos.
Palabras clave: modelo sintético ECG; filtros no lineales; morfología de las ondas.
Abstract
ECG signals have been used in cardiac pathology to detect disease heart. The main objective of this paper is to propose signal filtering techniques to reduce noise, extract information, to reconstruct the states and properties Morphological heartbeat. In addition, aims to represent the cardiac activity in a simple, informative, accurate, and easy to interpret for cardiologists. To achieve these objectives are proposed to implement the following algorithms: generic particle filter (GPF), resampling particle filter (RPF), unscented Kalman filter (UKF) and the unscented particle filter (UFP) considering the basic structure of synthetic dynamic model McSharry et al. (2003) [16]. The results show that filter performs very well in the reconstruction
of the states heart rate system, while introducing small variations in the variances of the noises of the equation observation, ie, the methods have the ability to reproduce the original signal the synthetic model simulated and the synthetic model with real data accurately. Finally evaluates the performance of the filters in terms of the empirical standard deviation, showing little variability among the estimated errors and fast execution of algorithms.
Keywords: synthetic ECG model; nonlinear filters; morphology of waves.
Mathematics Subject Classification: 62L12.
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Referencias
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[19] Paul, J; Reddy, M; Kumar, V. (2000) “A transform domain SVD filter for suppression of muscle noise artefacts in exercise ECG”, IEEE Trans. Biomed. Eng. 47(5): 654–663. [ Links ]
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[22] Sánchez, L., Infante, S; (2013) “Reconstruction of chaotic dynamic systems using nonlinear filters”, Chilean Journal of Statistics 4(1): 35–54. [ Links ]
[23] Sayadi, O; Sameni, R. (2007) “ECG denoising using parameters of ECG dynamical model as the states of an extended Kalman filter”, in: 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS, Lyon 22-26 Aug. 2007): 2548–2551. [ Links ]
[24] Sayadi, O; Shamsollahi,M. (2008a) “ECG denoising and compression using a modified extended Kalman filter structure”, IEEE Trans. on Biomedical Engineering 55(9): 2240–2248. [ Links ]
25 Sayadi, O; Shamsollahi, M. (2008b) “Model-based fiducial points extraction for baseline wandered electrocardiograms”, IEEE Trans. on Biomedical Engineering 55(1): 347–351. [ Links ]
[26] Sayadi, O; Shamsollahi, M. (2009) “A model-based Bayesian framework for ECG beat segmentation”. Journal of PhysiologicalMeasurement 30(3): 335–352. [ Links ]
[27] Sayadi, O; Shamsollahi, M; Clifford, G.D. (2010) “Synthetic ECG generation and Bayesian filtering using a Gaussian wave-based dynamical model”, Journal of PhysiologicalMeasurement 31(10): 1309–1329. [ Links ]
[28] Schreiber, T; Kaplan, D.T. (1996) “Nonlinear noise reduction for electrocardiograms”, Chaos 6(1): 87–92. [ Links ]
[29] Simon, D. (2006) Optimal State Estimation. Kalman, H%, and Nonlinear Approaches. JohnWiley & Sons, HobokenNJ. [ Links ]
[30] Storvik, G. (2002) “Paticle filters in state space models with the presence of unknown static parameters”, IEEE Trans. on Signal Processing 50(2): 281–289. [ Links ]
[31] van der Merwe, R.; Doucet, A; de Freitas, N; Wan, E. (2000) “The unscented particle filter”. Technical Report CUED/F-INFENG/TR 380, Engineering Department, Cambridge University. [ Links ]
[32] van der Merwe, R. (2004) Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models. PhD. Thesis, OGI School of Science & Engineering, Oregon Health and Science University, Portland. [ Links ]
[33] Vepa, R. (2010) “Nonlinear filtering of oscillatory measurements in cardiovascular applications”, Mathematical Problems in Engineering 2001, Article ID 808019, 18 pages. [ Links ]
[2] Arulampalam, S.; Maskell, S.; Gordon, N.; Clapp, T.A. (2002) “Tutorial on particle filters for on-line non linear/non Gaussian Bayesian tracking”, IEEE Transactions on Signal Processing 50(2): 174–188. [ Links ]
[3] Barros, A; Mansour, A; Ohnishi, N. (1998) “Removing artifacts from electrocardiographic signals using independent components analysis”, Neurocomputing 22(1-3): 173–186. [ Links ]
[4] Chen, Z. (2003) ”Bayesian filtering: From Kalman filters to particle filters, and beyond”, Technical report, Adaptive Systems Lab, McMaster University. [ Links ]
[5] Chui, C; Chen, G. (2009) Kalman Filtering with Real-Time Applications, Fourth Edition. Springer, Berlin. [ Links ]
[6] Clifford, G.; Tarassenko, L. (2001) “One pass training of optimal architecture auto associative neural network for detecting ectopic beats”, Electronics Letters 37(18): 1126–1127. [ Links ]
[7] Doucet, A.; Godsill, S.; Andrieu, C. (2000) ”On sequential Monte Carlo sampling methods for Bayesian filtering”, Statistics and Computing 10: 197–208. [ Links ]
[8] Doucet, A.; De Freitas, J.F.G.; Gordon, N., Eds. (2001) Sequential Monte Carlo Methods in Practice. SpringerVerlag, New York. [ Links ]
[9] Gordon, N.; Salmond, D.; Smith, A.F.M. (1993) “Novel approach to nonlinear non Gaussian Bayesian state estimation”, IEEE Proceedings F (Radar and Signal Processing) 140(2): 107–113. [ Links ]
[10] He, T; Clifford, G; Tarassenko, L. (2006) ”Application of independent component analysis in removing artefacts from the electrocardiogram”, Neural Comput. Appl. 15: 105–116. [ Links ]
[11] Julier, S. (2000) “The scaled unscented transformation”, IEEE Transactions on Automatic Control 45(3): 477–482. [ Links ]
[12] Julier, S; Uhlmann, J; Durrant, H. (2000) “A new method for nonlinear transformation of means and covariances in filter and estimators”, IEEE Transactions on Automatic Control 45(3): 477–482. [ Links ]
[13] Julier S.J.; Uhlmann, J.K. (2004) “Unscented filtering and nonlinear estimation”, Proceedings of the IEEE 92(3): 401–422. [ Links ]
[14] Kong, A; Liu, J; Wong, W. (1994) “Sequential imputations and Bayesian missing data problems”, Journal of the American Statistical Association 89: 278–288. [ Links ]
[15] Liu, J. (1996) “Metropolized independent sampling with comparison to rejection sampling and importance sampling”, Statistics and Computing 6: 113–119. [ Links ]
[16] McSharry, P; Clifford, G; Tarassenko, L; Smith, L. (2003) “A dynamical model for generating synthetic electrocardiogram signals”, IEEE Transactions on Biomedical Engineering 50(3): 289–294. [ Links ]
[17] Moody, G.; Mark, R. (1989) “QRS morphology representation and noise estimation using the Karhunen-Loeve transform”, Computers in Cardiology IEEE 16th Conference, Jerusalem: 269–272. [ Links ]
[18] Nikolaev, N; Nikolov, Z; Gotchev, A; Egiazarian, K. (2000) “Wavelet domain Wiener filtering for ECG denoising using improved signal estimate”, in: Proc. of ICASSP, IEEE Int. Conf. on Acoustics, Speech, and Sig. Proc., Vol.6: 3578–3581. [ Links ]
[19] Paul, J; Reddy, M; Kumar, V. (2000) “A transform domain SVD filter for suppression of muscle noise artefacts in exercise ECG”, IEEE Trans. Biomed. Eng. 47(5): 654–663. [ Links ]
[20] Potter M; Gadhok, N; Kinsner,W. (2002) “Separation performance of ICA on simulated EEG and ECG signals contaminated by noise”, in: Canadian Conference on Electrical and Computer Engineering (IEEE CCECE), 12-15 May, vol. 2: 1099–1104. [ Links ]
[21] Sameni, R; Shamsollahi, M; Jutten, C. (2005) “Filtering noisy ECG signals using the extended Kalman filter based on a modified dynamic ECG model”, Computers in Cardiology IEEE 32nd Conference, Lyon: 1017–1020. [ Links ]
[22] Sánchez, L., Infante, S; (2013) “Reconstruction of chaotic dynamic systems using nonlinear filters”, Chilean Journal of Statistics 4(1): 35–54. [ Links ]
[23] Sayadi, O; Sameni, R. (2007) “ECG denoising using parameters of ECG dynamical model as the states of an extended Kalman filter”, in: 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS, Lyon 22-26 Aug. 2007): 2548–2551. [ Links ]
[24] Sayadi, O; Shamsollahi,M. (2008a) “ECG denoising and compression using a modified extended Kalman filter structure”, IEEE Trans. on Biomedical Engineering 55(9): 2240–2248. [ Links ]
25 Sayadi, O; Shamsollahi, M. (2008b) “Model-based fiducial points extraction for baseline wandered electrocardiograms”, IEEE Trans. on Biomedical Engineering 55(1): 347–351. [ Links ]
[26] Sayadi, O; Shamsollahi, M. (2009) “A model-based Bayesian framework for ECG beat segmentation”. Journal of PhysiologicalMeasurement 30(3): 335–352. [ Links ]
[27] Sayadi, O; Shamsollahi, M; Clifford, G.D. (2010) “Synthetic ECG generation and Bayesian filtering using a Gaussian wave-based dynamical model”, Journal of PhysiologicalMeasurement 31(10): 1309–1329. [ Links ]
[28] Schreiber, T; Kaplan, D.T. (1996) “Nonlinear noise reduction for electrocardiograms”, Chaos 6(1): 87–92. [ Links ]
[29] Simon, D. (2006) Optimal State Estimation. Kalman, H%, and Nonlinear Approaches. JohnWiley & Sons, HobokenNJ. [ Links ]
[30] Storvik, G. (2002) “Paticle filters in state space models with the presence of unknown static parameters”, IEEE Trans. on Signal Processing 50(2): 281–289. [ Links ]
[31] van der Merwe, R.; Doucet, A; de Freitas, N; Wan, E. (2000) “The unscented particle filter”. Technical Report CUED/F-INFENG/TR 380, Engineering Department, Cambridge University. [ Links ]
[32] van der Merwe, R. (2004) Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models. PhD. Thesis, OGI School of Science & Engineering, Oregon Health and Science University, Portland. [ Links ]
[33] Vepa, R. (2010) “Nonlinear filtering of oscillatory measurements in cardiovascular applications”, Mathematical Problems in Engineering 2001, Article ID 808019, 18 pages. [ Links ]
* Departamento de Matemáticas, Centro de Análisis, Modelado y Tratamiento de Datos (CAMYTD), Facultad de Ciencia y Tecnología, Universidad de Carabobo. Valencia, Venezuela. E-Mail: sinfante@uc.edu.ve
† Departamento de Matemáticas, Facultad de Ciencias de la Educación, Universidad de Carabobo. Valencia, Venezuela. E-Mail: lsanchez8@uc.edu.ve
‡ Departamento de Matemáticas, Centro de Análisis, Modelado y Tratamiento de Datos (CAMYTD) , Facultad de Ciencia y Tecnología, Universidad de Carabobo. Valencia, Venezuela. E-Mail: fjcedeno@uc.edu.ve
Received: 7/May/2012; Revised: 19/May/2014; Accepted: 21/May/2014
