Sparse ECG Denoising with Generalized Minimax Concave Penalty

The electrocardiogram (ECG) is an important diagnostic tool for cardiovascular diseases. However, ECG signals are susceptible to noise, which may degenerate waveform and cause misdiagnosis. In this paper, the ECG noise reduction techniques based on sparse recovery are investigated. A novel sparse ECG denoising framework combining low-pass filtering and sparsity recovery is proposed. Two sparsity recovery algorithms are developed based on the traditional [Formula: see text]-norm penalty and the novel generalized minimax concave (GMC) penalty, respectively. Compared with the [Formula: see text]-norm penalty, the non-differentiable non-convex GMC penalty has the potential to strongly promote sparsity while maintaining the convexity of the cost function. Moreover, the GMC punishes large values less severely than [Formula: see text]-norm, which is utilized to overcome the drawback of underestimating the high-amplitude components for the [Formula: see text]-norm penalty. The proposed methods are evaluated on ECG signals from the MIT-BIH Arrhythmia database. The results show that underestimating problem is overcome by the proposed GMC-based method. The GMC-based method shows significant improvement with respect to the average of output signal-to-noise ratio improvement ([Formula: see text]), the average of root mean square error (RMSE) and the percent root mean square difference (PRD) over almost any given SNR compared with the classical methods, thus providing promising approaches for ECG denoising.