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

Abstract

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 non-stationary noise levels is studied as case study. While most ECG denoising techniques benefit from the pseudo-periodicity 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 Monte-Carlo 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.