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.
The ECGI inverse problem is still a common area of research. Since the results in the state of the art are not yet satisfactory, exploring new methods for the resolution of the inverse problem of electrocardiography is the main goal of this paper. To this purpose, we suggest to use temporal and spatial constraints to solve the inverse problem using neural networks methods. First, we use a time-delay neural network initialized with the spatial adjacency operator of the heart surface mesh. Then, we suggest a new approach to reconstruct the heart surface potential from the body surface potential using a spatial adaptation of time delay neural network. It consists on taking into account temporal and spatial dependence between potential measures. This allows to exploit the local and dynamic potential propagation properties. We test these approaches on simulated data. Results show that the new approach outperforms the classic time-delay neural network and has considerable improvements with respect to the state-of-the-art methods.
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