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

R. Molero, J. Reventós-Presmanes, I. Roca, L. Mont, A. Climent, M. Guillem
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Abstract

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.
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噪声对零阶吉洪诺夫正则化和l曲线优化心电图成像分辨率的影响
心电图成像(ECGI)可以通过反演电传播矩阵来计算心外膜的电活动,这可以通过正则化这个不适定问题来解决。本研究的目的是通过零阶吉洪诺夫和l曲线优化来评估噪声对信号选择正则化参数$(\lambda)$的影响。采用14例房颤(AF)模拟,计算不同噪声水平(3、10、20、30和40dB)下的ECGI。真实心律信号也用于计算$ECGI(3次心房颤动、2次心房扑动、3次心房起搏、3次心房窦性心律和3次室性心动过速)。对于模拟和患者,获得并比较了最大l曲线曲率和$\lambda$。在${A}F$模拟中,l曲线的最大曲率、噪声水平和最优$\lambda$是相关的。较高的噪声水平导致l曲线的曲率较小,并且选择较高的\ \lambda$值,从而减少计算ECGI时噪声的放大。AF的真实心脏信号在曲率和$\lambda$上的结果与模拟中探索的更高的噪声值$(3dB, \lambda > 10^{-6}$,曲率$< 1$)相似。信号噪声成比例地影响着ECGI的重建。给出了一种基于l曲线形状优化的可信赖ECGI图的方法。
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