Considering New Regularization Parameter-Choice Techniques for the Tikhonov Method to Improve the Accuracy of Electrocardiographic Imaging
Considering New Regularization Parameter-Choice Techniques for the Tikhonov Method to Improve the Accuracy of Electrocardiographic Imaging
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DOI：
10.3389/fphys.2019.00273
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发表时间：
2019-03-27
影响因子：
4
通讯作者：
Coudiere, Yves
中科院分区：
文献类型：
--
作者：
Chamorro-Servent, Judit;Dubois, Remi;Coudiere, Yves
心电图成像（ECGI）逆问题高度依赖于添加约束，这一过程称为正则化，因为问题是不适定的。当没有关于未知心外膜电位的先验信息时，Tikhonov正则化方法似乎是最常用的技术。在Tikhonov方法中，约束的权重由正则化参数确定。然而，正则化参数是问题和数据相关的，这意味着不同的数值模型或不同的临床数据可能需要不同的正则化参数。然后，我们需要尽可能多的正则化参数选择方法来验证它们。在这项工作中，我们解决了这个问题，表明离散皮卡德条件（DPC）可以指导一个很好的正则化参数选择的两个范数Tikhonov方法。我们还研究了两种技术的可行性：U曲线方法（尚未在心脏领域使用）和一种新的自动方法，称为ADPC，由于其基础上的DPC。这两种技术进行了测试，模拟和实验数据时，使用的基本解的方法作为一个数值模型。他们的功效进行了比较，在文献中，L曲线和CRESO方法的两个广泛使用的技术的功效。这些解决方案表明了新技术在心脏环境中的可行性，改善了重建心外膜电位的形态，并且在大多数情况下改善了其振幅。
The electrocardiographic imaging (ECGI) inverse problem highly relies on adding constraints, a process called regularization, as the problem is ill-posed. When there are no 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 problem and data dependent, meaning that different numerical models or different clinical data may require different regularization parameters. Then, we need to have as many regularization parameter-choice methods as techniques to validate them. In this work, we addressed this issue by showing that the Discrete Picard Condition (DPC) can guide a good regularization parameter choice for the two-norm Tikhonov method. We also studied the feasibility of two techniques: The U-curve method (not yet used in the cardiac field) and a novel automatic method, called ADPC due its basis on the DPC. Both techniques were tested with simulated and experimental data when using the method of fundamental solutions as a numerical model. Their efficacy was compared with the efficacy of two widely used techniques in the literature, the L-curve and the CRESO methods. These solutions showed the feasibility of 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.