Application of L0-norm regularization to epicardial potential reconstruction

Inverse problem of electrocardiography (ECG) has been extensively investigated as the estimated epicardial potentials (EPs) reflecting underlying myocardial activities. Traditionally, L2-norm regularization methods have been proposed to solve this ill-posed problem. But L2-norm penalty function inherently leads to considerable smoothing of the solution, which reduces the accuracy of distinguishing abnormalities and locating diseased regions. Directly using L1-norm penalty function, however, may greatly increase the computational complexity due to its non-differentiability. In this study, we present a smoothed L0 norm technique in order to directly solve the L0 norm constrained problem. Our method employs a smoothing function to make the L0 norm continuous. Extensive experiments on various datasets, including normal human data, isolated canine data, and WPW syndrome data, were conducted to validate our method. Epicardial potentials mapped during pacing were also reconstructed and visualized on the heart surface. Experimental results show that the proposed method reconstructs more accurate epicardial potentials compared with L1 norm and L2 norm based methods, demonstrating that smoothed L0 norm is a promising method for the noninvasive estimation of epicardial potentials.