QRS detection in noisy electrocardiogram using an adaptively regularized numerical differentiation method

QRS detection in noisy electrocardiograms (ECG) often requires the calculation of the signal's numerical differentiation without amplifying the noise. This study proposed and applied a numerical differentiation method based on adaptively weighted Tikhonov regularization (AWTR) in QRS detection. By adaptively weighting the terms of the summation in the regularization term, the AWTR-based method can accurately calculate the details in the derivative of noisy signals while maintaining smoothness. In particular, it does well in processing signals whose derivatives are continuous and have dramatic variations in some locations. When implemented on synthetic ECG signals with noise added, the AWTR-based numerical differentiation method achieves the highest accuracy compared with Tikhonov regularization and total-variation based ones. Based on this method, a QRS detection algorithm, which combines wavelet denoising, Hilbert transform, absolute-value transform, and adaptive threshold, is developed and evaluated. The algorithm can effectively emphasize QRS complexes in noisy ECG signals while suppressing the noise and other waveforms. The results pave the way for QRS detection with high accuracy. The sensitivity, positive predictivity and detection error rate of the algorithm implemented on the benchmark MIT-BIH Arrhythmia Database are 99.90%, 99.91%, and 0.20%, respectively, which are superior to most of the reported state-of-the-art methods.