Wavelet-domain group-sparse denoising method for ECG signals

In this paper, a group-sparse signal denoising approach is proposed, and both non-convex regularization and sparsity characteristics in wavelet domain are incorporated to estimate the electrocardiogram (ECG) signals with noise. To strongly promote wavelet sparsity, a parameterized non-convex penalty function is introduced, and the interval for the parameter is identified to guarantee the strict convexity of the total cost function. To retain the details of ECG signals, all the wavelet coefficients are estimated by minimizing certain single objective function, and thus the insignificant coefficients that do not survive wavelet thresholding can be maintained. The algorithm is solved based on the majorization–minimization optimization method, the alternating direction method of multipliers, and proximal method. The real collected ECG signals and MIT-BIH arrhythmia database are used to evaluate the effectiveness of the proposed wavelet-domain group-sparse method (WDGS) for ECG signal enhancement. By qualitative and quantitative analysis, it shows that our method can effectively suppress the undesired noise and keep the important morphology of ECG signals.