Online filtering using piecewise smoothness priors: Application to normal and abnormal electrocardiogram denoising

In this work, a block-wise extension of Tikhonov regularization is proposed for denoising smooth signals contaminated by wide-band noise. The proposed method is derived from a constrained least squares problem in two forms: 1) a block-wise fixed-lag smoother with smooth inter-block transitions applied in matrix form, and 2) a fixed-interval smoother applied as a forward-backward zero-phase filter. The filter response is maximally flat and monotonically decreasing, without any ripples in its pass-band. The method is also extended to smoothness of multiple smoothness orders, and its relationship with Lipschitz regularity and block-wise Wiener smoothing is also studied. The denoising of normal and abnormal electrocardiogram (ECG) signals in different stationary and nonstationary noise levels is studied as case study. While most ECG denoising techniques benefit from the pseudoperiodicity of the ECG, the developed technique is merely based on the smoothness assumption, which makes it a powerful method for both normal and abnormal ECG. The performance of the method is assessed by MonteCarlo simulations over three standard normal and abnormal ECG databases of different sampling rates, in comparison with bandpass filtering, wavelet denoising with various parameters, and Savitzky-Golay filters using Stein's unbiased risk estimate shrinkage scheme.