A Denoising Technique Based on SBWT and WATV: Application for ECG Denoising

In this chapter, we will detail our technique of ElectrocardiogramElectrocardiogram (ECG) (ECG) denoising, proposed in the literature. This technique is based on the application of Wavelet/Total VariationWavelet/Total-Variation (WATV) ( $${\text{WATV}}$$ )-based denoisingDenoising approach. This application is performed in the domain of the Stationary Bionic Wavelet TransformStationary Bionic Wavelet Transform ( $${\text{SBWT}}$$ ). This technique consists at the first step in applying the $${\text{SBWT}}$$ to the noisy ECG signal in order to have two noisy stationary bionic wavelet coefficients, $$wtb_1$$ and $$wtb_2$$ . The coefficient $$wtb_1$$ is a details one and is used for estimating the level of noise degrading the original ECG signal. The coefficient $$wtb_2$$ is an approximation one. The noise degrading the original ECGElectrocardiogram (ECG) signal is an Additive Gaussian White Noise (AGWN). We designates $$\sigma$$ as the noise level and is used for computing the threshold, $${\text{thr}}$$ , employed for the soft thresholdingThresholding of the coefficient $$wtb_1$$ and we obtain a denoised coefficient, $$wtd_1$$ . The denoising of $$wtb_2$$ is performed using $${\text{WATV}}$$ -based denoisingDenoising tecgnique and we obtain a denoised coefficient, $$wtd_2$$ . This WATVWavelet/Total-Variation (WATV)-based denoising approach also employs the noise level, $${\upsigma }$$ . The denoised ECG signal is finally obtained by applying the inverse of $${\text{SBWT}}$$ ( $${\text{SBWT}}^{ - 1}$$ ) to $$wtd_1$$ and $$wtd_2$$ . The performance of this proposed ECG denoising technique is proved by the results obtained from the calculations of the SNR (Signal to Noise Ratio), the MSE (Minimum Square Error), the MAE (Mean Absolute Error), the PSNR (Peak SNR), and the CC (Cross-Correlation).