A Novel Electrocardiogram Denoising Method based on Convex fused-Lasso Denoising with Non-Convex Regularization and Wavelet/Total Variation

Abstract

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).