Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data

The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularizati...
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Autor*in:	Amel Karoui [verfasserIn] Laura Bear [verfasserIn] Pauline Migerditichan [verfasserIn] Nejib Zemzemi [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	inverse problem Tikhonov regularization L1-norm regularization regularization parameter method of fundamental solutions finite element method

Übergeordnetes Werk:	In: Frontiers in Physiology - Frontiers Media S.A., 2011, 9(2018)
Übergeordnetes Werk:	volume:9 ; year:2018

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3389/fphys.2018.01708

Katalog-ID:	DOAJ075062658

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520			\|a The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization.
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allfields	10.3389/fphys.2018.01708 doi (DE-627)DOAJ075062658 (DE-599)DOAJc5ec9885648e4ccfa2d62332087060a7 DE-627 ger DE-627 rakwb eng QP1-981 Amel Karoui verfasserin aut Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization. inverse problem Tikhonov regularization L1-norm regularization regularization parameter method of fundamental solutions finite element method Physiology Amel Karoui verfasserin aut Amel Karoui verfasserin aut Laura Bear verfasserin aut Pauline Migerditichan verfasserin aut Pauline Migerditichan verfasserin aut Nejib Zemzemi verfasserin aut Nejib Zemzemi verfasserin aut Nejib Zemzemi verfasserin aut In Frontiers in Physiology Frontiers Media S.A., 2011 9(2018) (DE-627)631498788 (DE-600)2564217-0 1664042X nnns volume:9 year:2018 https://doi.org/10.3389/fphys.2018.01708 kostenfrei https://doaj.org/article/c5ec9885648e4ccfa2d62332087060a7 kostenfrei https://www.frontiersin.org/article/10.3389/fphys.2018.01708/full kostenfrei https://doaj.org/toc/1664-042X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2018
spelling	10.3389/fphys.2018.01708 doi (DE-627)DOAJ075062658 (DE-599)DOAJc5ec9885648e4ccfa2d62332087060a7 DE-627 ger DE-627 rakwb eng QP1-981 Amel Karoui verfasserin aut Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization. inverse problem Tikhonov regularization L1-norm regularization regularization parameter method of fundamental solutions finite element method Physiology Amel Karoui verfasserin aut Amel Karoui verfasserin aut Laura Bear verfasserin aut Pauline Migerditichan verfasserin aut Pauline Migerditichan verfasserin aut Nejib Zemzemi verfasserin aut Nejib Zemzemi verfasserin aut Nejib Zemzemi verfasserin aut In Frontiers in Physiology Frontiers Media S.A., 2011 9(2018) (DE-627)631498788 (DE-600)2564217-0 1664042X nnns volume:9 year:2018 https://doi.org/10.3389/fphys.2018.01708 kostenfrei https://doaj.org/article/c5ec9885648e4ccfa2d62332087060a7 kostenfrei https://www.frontiersin.org/article/10.3389/fphys.2018.01708/full kostenfrei https://doaj.org/toc/1664-042X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2018
allfields_unstemmed	10.3389/fphys.2018.01708 doi (DE-627)DOAJ075062658 (DE-599)DOAJc5ec9885648e4ccfa2d62332087060a7 DE-627 ger DE-627 rakwb eng QP1-981 Amel Karoui verfasserin aut Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization. inverse problem Tikhonov regularization L1-norm regularization regularization parameter method of fundamental solutions finite element method Physiology Amel Karoui verfasserin aut Amel Karoui verfasserin aut Laura Bear verfasserin aut Pauline Migerditichan verfasserin aut Pauline Migerditichan verfasserin aut Nejib Zemzemi verfasserin aut Nejib Zemzemi verfasserin aut Nejib Zemzemi verfasserin aut In Frontiers in Physiology Frontiers Media S.A., 2011 9(2018) (DE-627)631498788 (DE-600)2564217-0 1664042X nnns volume:9 year:2018 https://doi.org/10.3389/fphys.2018.01708 kostenfrei https://doaj.org/article/c5ec9885648e4ccfa2d62332087060a7 kostenfrei https://www.frontiersin.org/article/10.3389/fphys.2018.01708/full kostenfrei https://doaj.org/toc/1664-042X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2018
allfieldsGer	10.3389/fphys.2018.01708 doi (DE-627)DOAJ075062658 (DE-599)DOAJc5ec9885648e4ccfa2d62332087060a7 DE-627 ger DE-627 rakwb eng QP1-981 Amel Karoui verfasserin aut Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization. inverse problem Tikhonov regularization L1-norm regularization regularization parameter method of fundamental solutions finite element method Physiology Amel Karoui verfasserin aut Amel Karoui verfasserin aut Laura Bear verfasserin aut Pauline Migerditichan verfasserin aut Pauline Migerditichan verfasserin aut Nejib Zemzemi verfasserin aut Nejib Zemzemi verfasserin aut Nejib Zemzemi verfasserin aut In Frontiers in Physiology Frontiers Media S.A., 2011 9(2018) (DE-627)631498788 (DE-600)2564217-0 1664042X nnns volume:9 year:2018 https://doi.org/10.3389/fphys.2018.01708 kostenfrei https://doaj.org/article/c5ec9885648e4ccfa2d62332087060a7 kostenfrei https://www.frontiersin.org/article/10.3389/fphys.2018.01708/full kostenfrei https://doaj.org/toc/1664-042X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2018
allfieldsSound	10.3389/fphys.2018.01708 doi (DE-627)DOAJ075062658 (DE-599)DOAJc5ec9885648e4ccfa2d62332087060a7 DE-627 ger DE-627 rakwb eng QP1-981 Amel Karoui verfasserin aut Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization. inverse problem Tikhonov regularization L1-norm regularization regularization parameter method of fundamental solutions finite element method Physiology Amel Karoui verfasserin aut Amel Karoui verfasserin aut Laura Bear verfasserin aut Pauline Migerditichan verfasserin aut Pauline Migerditichan verfasserin aut Nejib Zemzemi verfasserin aut Nejib Zemzemi verfasserin aut Nejib Zemzemi verfasserin aut In Frontiers in Physiology Frontiers Media S.A., 2011 9(2018) (DE-627)631498788 (DE-600)2564217-0 1664042X nnns volume:9 year:2018 https://doi.org/10.3389/fphys.2018.01708 kostenfrei https://doaj.org/article/c5ec9885648e4ccfa2d62332087060a7 kostenfrei https://www.frontiersin.org/article/10.3389/fphys.2018.01708/full kostenfrei https://doaj.org/toc/1664-042X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2003 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 9 2018
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callnumber-first	Q - Science
author	Amel Karoui
spellingShingle	Amel Karoui misc QP1-981 misc inverse problem misc Tikhonov regularization misc L1-norm regularization misc regularization parameter misc method of fundamental solutions misc finite element method misc Physiology Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data
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topic_title	QP1-981 Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data inverse problem Tikhonov regularization L1-norm regularization regularization parameter method of fundamental solutions finite element method
topic	misc QP1-981 misc inverse problem misc Tikhonov regularization misc L1-norm regularization misc regularization parameter misc method of fundamental solutions misc finite element method misc Physiology
topic_unstemmed	misc QP1-981 misc inverse problem misc Tikhonov regularization misc L1-norm regularization misc regularization parameter misc method of fundamental solutions misc finite element method misc Physiology
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title	Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data
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title_full	Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data
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title_sort	evaluation of fifteen algorithms for the resolution of the electrocardiography imaging inverse problem using ex-vivo and in-silico data
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title_auth	Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data
abstract	The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization.
abstractGer	The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization.
abstract_unstemmed	The electrocardiographic imaging inverse problem is ill-posed. Regularization has to be applied to stabilize the problem and solve for a realistic solution. Here, we assess different regularization methods for solving the inverse problem. In this study, we assess (i) zero order Tikhonov regularization (ZOT) in conjunction with the Method of Fundamental Solutions (MFS), (ii) ZOT regularization using the Finite Element Method (FEM), and (iii) the L1-Norm regularization of the current density on the heart surface combined with FEM. Moreover, we apply different approaches for computing the optimal regularization parameter, all based on the Generalized Singular Value Decomposition (GSVD). These methods include Generalized Cross Validation (GCV), Robust Generalized Cross Validation (RGCV), ADPC, U-Curve and Composite REsidual and Smoothing Operator (CRESO) methods. Both simulated and experimental data are used for this evaluation. Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. Finally, the use of FEM-L1-Norm combined with RGCV provides robust results in the pacing site localization.
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title_short	Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data
url	https://doi.org/10.3389/fphys.2018.01708 https://doaj.org/article/c5ec9885648e4ccfa2d62332087060a7 https://www.frontiersin.org/article/10.3389/fphys.2018.01708/full https://doaj.org/toc/1664-042X
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Results show that the RGCV approach provides the best results to determine the optimal regularization parameter using both the FEM-ZOT and the FEM-L1-Norm. However for the MFS-ZOT, the GCV outperformed all the other regularization parameter choice methods in terms of relative error and correlation coefficient. Regarding the epicardial potential reconstruction, FEM-L1-Norm clearly outperforms the other methods using the simulated data but, using the experimental data, FEM based methods perform as well as MFS. 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Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data

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