Electrocardiogram Denoising Based on SWT and WATV Using ANNs

This paper introduces an innovative electrocardiogram (\({\text{ECG}}\)) denoising technique based on stationary wavelet transform (\(SWT)\) and wavelet/total variation (WATV). In this technique, we also use two different artificial neural networks (\(ANNs\)) to determine two ideal thresholds, \(thr_{1}\) and \(thr_{2}\). The latter is used for the soft thresholding of a noisy details coefficient, \(cdb_{2}\), to obtain a denoised coefficient, \(cdd_{2}\). The threshold \(thr_{1}\) is used for the soft thresholding of a noisy details coefficient, \(cdb_{1}\), yielding a denoised coefficient, \(cdd_{1} .{ }\) The coefficient \(cdb_{1}\) and a noisy approximation coefficient, \(cab_{1}\), are obtained by applying \(SWT\) to the noisy ECG signal. The coefficient \(cdb_{2}\) and another noisy approximation coefficient, \(cab_{2}\), are obtained by applying \(SWT\) to \(cab_{1}\). In this proposed ECG denoising system, we also apply a WATV-based denoising technique to \(cab_{2}\) to obtain a denoised approximation coefficient, \(cad_{2}\). This WATV-based denoising technique requires the estimation of the level of the noise corrupting the clean ECG signal. This noise is additive Gaussian white noise (AGWN) and its level is denoted as \(\sigma\), which is estimated from \(cdb_{1}\). After that, the inverse of \(SWT\) (\(SWT^{ - 1}\)) is applied to \(cdd_{2}\) and \(cad_{2}\) to obtain a denoised approximation coefficient, \(cad_{1}\). Subsequently, we apply \(SWT^{ - 1}\) to \(cdd_{1}\) and \(cad_{1}\) to finally obtain the denoised ECG signal. The performance of this proposed ECG denoising technique is proven by the results obtained after computing the signal-to-noise ratio (\(SNR\)), the peak SNR (\(PSNR\)), the mean square error (\(MSE\)), the mean absolute error (\(MAE\)) and the cross-correlation (\(CC\)).