A New Technique of ECG Denoising based on LWT and Total Variation Minimization ECG Denoising

In this paper we propose a new technique of Electrocardiogram (ECG) denoising. This technique is based on Lifting Wavelet Transform
$(LWT)$
and Total variation based denoising technique using majorization-minimization. It consists at the first step in applying the
$LWT$
to the noisy ECG signal in order to obtain three noisy coefficients,
$cA_{2}, cD_{2}$
and
$cD_{1}$
. The coefficients
$cD_{2}$
and
$cD_{1}$
are respectively the details coefficient at level 2 and the details one at level 1 and are denoised applying soft thresholding and we obtain two denoised coefficients,
$cDd_{2}$
and
$cDd_{1}$
. The coefficient
$cA_{2}$
is the approximation one and is denoised applying the Total variation based denoising technique using majorization-minimization and we obtain a denoised coefficient,
$cAd_{2}$
. The denoised ECG signal is finally obtained from the application of the LWT inverse (
$(LWT)^{-1}$
) to the denoised coefficients.,
$cDd_{1}, cDd_{2}$
and
$cAd_{2}$
. The performance of the proposed ECG denoising technique is proved by the results obtained from the computation of the Signal to Noise Ratio (SNR), the Peak SNR (PSNR), the Mean Absolute Error (MAE), the Mean Square Error (MSE) and the Cross-Correlation (CC).