Evaluation of 2-norm versus sparsity regularization in spline-based joint reconstruction of epicardial and endocardial potentials from body-surface measurements

Cardiac electrical imaging, reconstruction of cardiac electrical activity from body surface potentials, has gained increasing clinical interest as a noninvasive imaging modality for underlying electrophysiological phenomena. We have previously presented an approach using 1) a transmural regularization to improve the joint reconstruction of electrical potentials on both the inner and outer surface of the ventricles; and 2) a nonlinear low-order dynamic spline-based parameterization to provide temporal regularization. This approach was tested for localizing endocardial pacing locations obtained from healthy hearts during catheter-based stimulation, using imprecise thorax geometry derived from limited computed tomographic scans. Results were promising, but the reconstructed solutions were overly smooth in space and time. Recently, L1-norm based spatial sparsity methods such as total-variation regularization have been reported to return more realistically sharp solutions in cardiac electrical imaging. In this paper, we compare and evaluate the performance of L2-norm based Tikhonov and L1-norm based total-variation regularization in conjunction with the spline parameterization and the transmural regularization. Numerical experiments were conducted on three subjects, each with multiple (~ 20) endocardial pacing sites and evaluated against true pacing locations reported by the CARTO catheter mapping system. Variability was observed in the performance of the two methods across both pacing sites and subjects. However, the dependence of the results on subjects and ventricular pacing locations suggests that there is some correlation between the results and the specific geometry in each case. In our future work, we will investigate the approach of automatically inferring an optimal regularization norm from the data rather than fixing it a priori.