A Multi-Disciplinary Approach to Solve the Inverse Problem of Electro- and Magnetocardiography

在心电图（ECG）中，通过解读体表测量的电压来研究心脏。通过增加传感器数量和利用物理和数学方法对信号进行建模，可以提高心电信号的空间精度。在ECG反问题中，目的是从体表测得的信号中估计出心脏电源的来源或心脏表面的电位。这个问题是病态的：需要简化假设、先验信息和正则化。该项目的目的是通过开发解决心电图逆问题的方法来提高心电图作为心脏诊断工具的价值。第一项研究将集中在使用基于模型的时空正则化技术来提高重建质量。第二种方法旨在评估在存在不完整模型和数据的情况下，电和磁心动图成像重建临床相关信息的能力。在第三个方面，重点将放在新的数学方法上，比如使求解器更快、更有效，这可以通过对大规模病态问题的分解来实现。另一个方面是使用不同的误差规范和正则化方案。

In electrocardiography (ECG), the heart is studied by interpreting voltages measured on the body surface. The spatial accuracy of the ECG can be improved by adding more sensors and by modeling the signals with the help of physics and mathematics. In the inverse problem of ECG, the aim is to estimate the sources of the cardiac electric sources or the electric potential on the surface of the heart from the measured signal at the body surface. This problem is illposed: simplifying assumptions, a-priori information, and regularization are needed.The aim of this project is to increase the value of ECG as a tool for cardiac diagnosis by developing methods for solving the inverse problem of electrocardiography.The first research lead will concentrate on an increase in the reconstruction quality using model-based spatio-temporal regularization techniques. The second approach aims to assess the capability of electro- and magnetocardiographic imaging of reconstructing clinically relevant information in the presence of incomplete models and data. In a third lead, the focus will be on new mathematical approaches like making the solver faster and more effective, which can be achieved by a decomposition of the large-scale ill-conditioned problem. Another aspect is the use of different error norms and regularization schemes.