Fast and Sample Accurate R-Peak Detection for Noisy ECG Using Visibility Graphs

More than a century has passed since Einthoven laid the foundation of modern electrocardiography and in recent years, driven by the advance of wearable and low budget devices, a sample accurate detection of R-peaks in noisy ECG-signals has become increasingly important. To accommodate these demands, we propose a new R-peak detection approach that builds upon the visibility graph transformation, which maps a discrete time series to a graph by expressing each sample as a node and assigning edges between intervisible samples. The proposed method takes advantage of the high connectivity of large, isolated values to weight the original signal so that R-peaks are amplified while other signal components and noise are suppressed. A simple thresholding procedure, such as the widely used one by Pan and Tompkins, is then sufficient to accurately detect the R-peaks. The weights are computed for overlapping segments of equal size and the time complexity is shown to be linear in the number of segments. Finally, the method is benchmarked against existing methods using the same thresholding on a noisy and sample accurate database. The results illustrate the potential of the proposed method, which outperforms common detectors by a significant margin.

I. Introduction

Detecting R-peaks in ECG-signals is required for many applications in healthcare (e.g., [1], [2]) and the topic has been studied for more than four decades. While algorithms for peak detection come in great quantity (e.g., [3]–[11]), there is no single best method and there is still room for improvements, particularly for ECG measurements during movement and exercise as well as for the sample accurate detection of the R-peaks. Current popular benchmark peak detection algorithms are built upon, e.g., the derivative [5], the stationary wavelet transform (SWT) [6], matched filters [7], [3] and neural networks [4], [10]. In this work, we propose a new peak detection approach that builds upon the visibility graph transformation. The key idea is to first represent the sampled data as a network of the sampling points that captures local features and nonstationary properties of the signal at hand and subsequently to compute weights for each sampling point that amplify R-peaks and dampen other signal components and noise. The peaks can then be detected using an established thresholding scheme, e.g., the one proposed by Pan and Tompkins [5].