A Novel ECG Enhancement and QRS Detection Scheme Based on the 1-D High-Order Non-convex Total Variation Denoising

Electrocardiogram (ECG) is a crucial tool for diagnosing cardiovascular diseases, while it is typically contaminated by numerous sorts of noise or artifacts, for instance, non-stationary noise because of muscle contraction. In order to reduce the noise components overlapping with signal spectrum, a novel ECG enhancement framework is proposed which incorporates the low-pass filter combined with the 1-D high-order total variation denoising model based on the non-convex penalty defined by the Moreau envelope. Compared with the traditional ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{1}$$\end{document}-norm penalty, the non-differentiable non-convex penalty has the potential to strongly promote signal’s sparsity and avoid the underestimation of the high-amplitude elements while maintaining the convexity of the cost function. Meanwhile, the high-order derivative sparsity as an inherent property of the piecewise smooth signal could accurately detect true jump discontinuities, averting the stair casing effect. Finally, simulations on the denoising problem and the QRS detection are made in the synthetic ECG signal and real ECG signals from the MIT-BIH Arrhythmia database both with additive Gaussian white noise. Experimental results demonstrate that the proposed method which is based on the 1-D high-order total variation and non-convex penalty performs better than the first-order-based as well as ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{1}$$\end{document}-norm penalty-based methods.