Application of L1-Norm Regularization to Epicardial Potential Solution of the Inverse Electrocardiography Problem

The electrocardiographic inverse problem of computing epicardial potentials from multi-electrode body-surface ECG measurements, is an ill-posed problem. Tikhonov regularization is commonly employed, which imposes penalty on the L2-norm of the potentials (zero-order) or their derivatives. Previous work has indicated superior results using L2-norm of the normal derivative of the solution (a first order regularization). However, L2-norm penalty function can cause considerable smoothing of the solution. Here, we use the L1-norm of the normal derivative of the potential as a penalty function. L1-norm solutions were compared to zero-order and first-order L2-norm Tikhonov solutions and to measured ‘gold standards’ in previous experiments with isolated canine hearts. Solutions with L1-norm penalty function (average relative error [RE] = 0.36) were more accurate than L2-norm (average RE = 0.62). In addition, the L1-norm method localized epicardial pacing sites with better accuracy (3.8 ± 1.5 mm) compared to L2-norm (9.2 ± 2.6 mm) during pacing in five pediatric patients with congenital heart disease. In a pediatric patient with Wolff–Parkinson–White syndrome, the L1-norm method also detected and localized two distinct areas of early activation around the mitral valve annulus, indicating the presence of two left-sided pathways which were not distinguished using L2 regularization.