Regularization Matrices for Inverse Electrocardiography

In a recent series of papers we proposed a new class of methods, the generalized eigensystem (GES) methods, for solving the inverse problem of electrocardiography. In this paper, we compare zero, first, and second order regularized GES methods to zero, first, and second order Tikhonov methods. Results from higher order regularization depend heavily on the exact form of the regularization operator, and operators generated by finite element techniques give the most accurate and consistent results. The GES techniques always produce smaller average relative errors than the Tikhonov techniques, but as the regularization order increases the difference in average relative errors between the two techniques becomes less pronounced.