Impact of Noise on Electrocardiographic Imaging Resolution with Zero Order Tikhonov Regularization and L-Curve Optimization

Electrocardiographic Imaging (ECGI) allows computing the electrical activity in the epicardium by inverting the electrical propagation matrix, which can be solved by regularizing this ill-posed problem. The objective of this study is to evaluate the effects of noise on the signals in the selection of the regularization parameter $(\lambda)$ by zero-order Tikhonov and L-curve optimization. Fourteen atrial fibrillation (AF) simulations were used for computing the ECGI with different noise levels (3, 10, 20, 30, and 40dB). Signals of real cardiac rhythms were also used to compute the $ECGI(3\ AF, 2$ atrial flutters, 3 atrial pacing, 3 atrial sinus rhythm and 3 ventricular tachycardia). For simulations and patients, maximum L-curve curvature and $\lambda$ were obtained and compared. The maximum curvature of the L-curve, noise level and optimal $\lambda$ correlated for ${A}F$ simulations. Higher levels of noise resulted in smaller curvatures of the L-curve and the selection of higher values $of\ \lambda$, reducing the amplification of noise when computing ECGI. Real cardiac signals of AF presented similar results in curvature and $\lambda$ as the higher values of noise explored in simulations $(3dB, \lambda > 10^{-6}$, curvature $< 1$). The noise of the signal proportionally affects to the reconstruction of ECGI. The given results show a methodology to obtain trustable ECGI maps based on the shape of the L-curve optimization.