  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.
