Considering New Regularization Parameter-Choice Techniques for the Tikhonov Method to Improve the Accuracy of Electrocardiographic Imaging - Chamorro-Servent, Judit; Dubois, Rémi; Coudière, Yves (Frontiers in Physiology, 2019)
The electrocardiographic imaging (ECGI) inverse problem highly relies on adding constraints, a process called regularization, as the problem is ill-posed. When there is not prior information provided about the unknown epicardial potentials, the Tikhonov regularization method seems to be the most commonly used technique. In the Tikhonov approach the weight of the constraints is determined by the regularization parameter. However, the regularization parameter is very problem and data dependent, meaning that different numerical models or different clinical data may require different regularization parameters. Then, we need to have as much as regularization parameter-choice methods at our hands and techniques to validate them. In this work, we address this issue by showing that the Discrete Picard Condition (DPC) can guide us to choose a good regularization parameter for the two-norm Tikhonov method. We also study the feasibility of two techniques: The U-curve method (not used yet in the cardiac field) and a novel automatic method, called ADPC due its basis on the DPC. Both techniques are tested with simulated and experimental data when using the method of fundamental solutions as a numerical model. Their efficacy is compared with the efficacy of two widely used techniques in the literature, the L-curve and the CRESO methods. Solutions show the feasibility of both the new techniques in the cardiac setting, an improvement of the morphology of the reconstructed epicardial potentials, and in most of the cases of their amplitude.