Level-dependent wavelet denoising:: Application to very noisy ECG signals

We present in this work an algorithm allowing the filtering of very noisy ECG signal, corrupted by a white Gaussian noise (WGN) with an SNR of around 0 dB. Our algorithm tends to solve the drawbacks faced to the classical wavelet denoising approach using the 'VisuShrink' threshold calculus method and the hard thresholding strategy, in the case of very noisy ECG signal, mainly the R wave distortion. Our key idea is to pass, first, the noisy signal through the classical low pass Butterworth filter, and, next, to use level-dependent threshold calculated basing, mainly, on the 'VisuShrink' methodology given by: Tj=(2*log(Nj))1/2*median(vertical bar Cj vertical bar)/0.6745. Our study demonstrates that the optimal value of the Ni is the length of corresponding detail level (j) while the median(vertical bar Cj vertical bar) value is kept constant, along the different denoising levels, and is computed at the lowest resolution DWT, i.e. Cj=cD1 (the 1st level detail coefficients) of the very noisy ECG signal. The obtained results of applying our algorithm to the record '100.dat' of the MIT-BIH Arrhythmia Database, corrupted with a WGN of an SNR of 0 dB, provides an output SNR of around 4.25 dB and an MSE of 0.0016. A comparative study using the classical wavelet denoising process, at 2 successive levels (4th, and 5th) and the classical low pass Butterworth filter provides the output SNRs of (3.65, 3.37, and 3.74 dBs) and mean square error (MSE) values of (0.0017, 0.0018, and 0.0018) respectively. These obtained results demonstrate the superior performance of our algorithm regarded to the set of the tested denoising approaches.