本文介绍了一种基于平稳小波变换(\(SWT)\)和小波/总变分(WATV)的创新心电图( \({\text{ECG}}\) )去噪技术。在该技术中,我们还使用两个不同的人工神经网络(\(ANNs\))来确定两个理想阈值\(thr_{1}\)和\(thr_{2}\)。后者用于对噪声细节系数\(cdb_{2}\)进行软阈值处理,以获得去噪系数\(cdd_{2}\)。阈值\(thr_{1}\)用于对噪声细节系数\(cdb_{1}\)进行软阈值处理,产生去噪系数\(cdd_{1} .{ }\)系数\ (cdb_{1}\)和噪声近似系数\(cab_{1}\)是通过将\(SWT\)应用于噪声 ECG 信号而获得的。系数\(cdb_{2}\)和另一个噪声近似系数\(cab_{2}\)是通过将\(SWT\)应用于\(cab_{1}\)获得的。在这个提出的心电图去噪系统中,我们还将基于 WATV 的去噪技术应用于\(cab_{2}\)以获得去噪近似系数\(cad_{2}\)。这种基于 WATV 的降噪技术需要估计破坏干净 ECG 信号的噪声水平。该噪声是加性高斯白噪声 (AGWN),其级别表示为\(\sigma\),由\(cdb_{1}\)估计。之后,将\(SWT\)的逆( \(SWT^{ - 1}\) ) 应用于\(cdd_{2}\)和\(cad_{2}\)以获得去噪近似系数,\(cad_{1}\)。随后,我们将\(SWT^{ - 1}\)应用于\(cdd_{1}\)和\(cad_{1}\),最终获得去噪后的心电信号。计算信噪比 ( \(SNR\) )、峰值 SNR ( \(PSNR\) )、均方误差 ( \(MSE ) 后获得的结果证明了所提出的心电图去噪技术的性能\) )、平均绝对误差 ( \(MAE\) ) 和互相关 ( \(CC\) )。
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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 (\(CC\)).