Improved parameter choice methods and temporal filtering for the generalized eigensystem method applied to the inverse problem of electrocardiography

We have previously proposed the generalized eigensystem (GES) method as a modal expansion method for estimating electrical potentials on the heart outer surface from measurements of electrical potentials on the body surface. In this paper, we present an alternative formulation of GES more like that of classical Tikhonov regularization where a single continuous parameter needs to be chosen. We then compare this formulation of GES with zero order Tikhonov regularization on data collected from a swine experiment with the swine heart paced from six different sites. Of the two algorithms used to estimate the regularization parameters, the composite residual and smoothing operator (CRESO) generally outperforms the generalized cross validation (GCV) for both GES and Tikhonov. Although the inverse problems are solved at each time instant independently, we also incorporate temporal information by moving average filtering the estimates, and this is more effective for the GES methods than for Tikhonov. In general, the epicardial estimates using the GES method are more accurate than the estimates generated using zero order Tikhonov regularization.