In this paper, we propose a new Electrocardiogram (ECG) denoising approach based on Convex fused lasso Denoising with non-convex regularization and Wavelet/Total Variation (WATV). This approach consists at first step of applying the Discrete Wavelet Transform (DWT) to the noisy ECG signal for obtaining a noisy approximation coefficient, cAb1 and a noisy details coefficient, cDb1. The latter is denoised by soft thresholding and we obtain a denoised details coefficient, cDd1. The second step of this approach consists of applying the DWT to cAb1 in order to obtain a noisy approximation coefficient, cAb2 and a noisy details coefficient, cDb2. The latter is denoised by Convex fused lasso denoising with non-convex regularization and we obtain a denoised details coefficient, cDd2. The coefficient, cAb2, is denoised by WATV based denoising technique and we obtain a denoised coefficient, cAd2. The inverse of DWT is then applied to cDd2 and cAd2 in order to obtain a denoised approximation coefficient, cAd1. The inverse of DWT is again applied to cDd1 and cAd1 for obtaining finally a denoised ECG signal. The performance of this proposed approach is proved by the computation of SNR, the PSNR, the MSE, the Mean Absolute Error (MAE), and the Cross-Correlation (CC).

In this paper, a new technique of Electrocardiogram (ECG) denoising, is introduced and is based on Transformation Matrix for Non-Decimated Wavelet Transform (WT) and Wavelet/Total Variation (WATV) Denoising. It firstly consists of applying twice the Discrete Wavelet Transform (DWT) to the noisy ECG in order to obtain three wavelet coefficients which are the approximation coefficient, cA1 (at level 2) and two details coefficients, cD (at level 1) and cD1 (at level 2). Then, the two coefficients, cD and cD1 are denoised by applying the Transformation Matrix for Non-Decimated WT and we obtain two denoised coefficients, cDd and cDd1. The coefficient, cA1, is also denoised by applying the WATV Denoising and we obtain a third denoised coefficient, cAd1. Finally, the inverse of DWT is twice applied to the three denoised coefficients, cDd, cDd1and cAd1 in order to obtain the denoised ECG signal. The results obtained from the computations of SNR (Signal to Noise Ratio), PSNR (Peak SNR), MSE (Mean Square Error), MAE (Mean Absolute Error) and Cross-Correlation (CC), show the performance of this ECG denoising approach, proposed in this work.