Regularized-truncation approach in inverse problem of electrocardiography

In the inverse problem of electrocardiography, an overspecified Cauchy condition for an elliptic operator must be satisfied under realistic conditions for which (i) the geometry of the problem domain has an irregular shape, and (ii) the observation data (volume conductor properties and thoracic potentials) are perturbed by noise. Since numerical treatment is needed, this problem is reduced to one with a finite dimension and the instability of this discretized inverse problem becomes more important. Here, the authors use the generalized singular value decomposition to derive an inverse method based on revising the space of the regularized solution. This method, regularized-truncation, is then applied to simulated data using a 3D finite element model of a human torso, and the inverse solutions are compared with those obtained using Tikhonov regularization