论文标题
一个涉及粘性艾科纳尔方程的逆问题，具有电生理学的应用
An inverse problem involving a viscous Eikonal equation with applications in electrophysiology
论文作者
论文摘要
在这项工作中，我们讨论了基于边界观测值的粘性艾科纳尔方程的心脏激活瞬间的重建。该问题被称为最小二乘问题，并通过Levenberg Marquardt方法的投影版本解决。此外，我们分析了状态方程的井功能，并得出了最小二乘相对于激活瞬变的梯度。在数值示例中，我们还进行了一个实验，其中激活位点和激活瞬间的位置是根据https://link.springer.com/article/10.1007/s00285-0285-019-019-019-01419-3共同重建了形状梯度方法的重建。我们能够相对于噪声水平重建激活速度以及激活的位置。
In this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as an least squares problem and solved by a projected version of the Levenberg Marquardt method. Moreover, we analyze the wellposeness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from https://link.springer.com/article/10.1007/s00285-019-01419-3. We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.
