  Noninvasive reconstruction of cardiac electrical activity from surface
electrocardiograms (ECG) involves solving an ill-posed inverse problem. Cardiac
electrophysiological (EP) models have been used as important a priori knowledge
to constrain this inverse problem. However, the reconstruction suffer from
inaccuracy and uncertainty of the prior model itself which could be mitigated
by estimating a priori model error. Unfortunately, due to the need to handle an
additional large number of unknowns in a problem that already suffers from
ill-posedness, model error estimation remains an unresolved challenge. In this
paper, we address this issue by modeling and estimating the a priori model
error in a low dimensional space using a novel sparse prior based on the
variational approximation of L0 norm. This prior is used in a posterior
regularized Bayesian formulation to quantify the error in a priori EP model
during the reconstruction of transmural action potential from ECG data. Through
synthetic and real-data experiments, we demonstrate the ability of the
presented method to timely capture a priori model error and thus to improve
reconstruction accuracy compared to approaches without model error correction.
