A new method for choosing the regularization parameter in time-dependent inverse problems and its application to magnetocardiography

The current density estimation on the epicardial surface of the heart based on electrocardiographic and magnetocardiographic measurements is one example of an ill-posed inverse problem. Commonly, zeroth-order Tikhonov regularization is applied to solve such problems. A few methods exist for the determination of the critical regularization parameter. However, none of these methods performed sufficiently in our application. In this paper, we propose a new method for choosing a regularization parameter for a time interval. Our basic assumption for this method is that the optimal solution norm must reflect the temporal properties of the magnetic energy. The performance of our method is tested both on simulated data and patient data.