Objective: Gaussian Processes (GP)-based filters, which have been effectively used for various applications including electrocardiogram (ECG) filtering can be computationally demanding and the choice of their hyperparameters is typically ad hoc. Methods: We develop a data-driven GP filter to address both issues, using the notion of the ECG phase domain -- a time-warped representation of the ECG beats onto a fixed number of samples and aligned R-peaks, which is assumed to follow a Gaussian distribution. Under this assumption, the computation of the sample mean and covariance matrix is simplified, enabling an efficient implementation of the GP filter in a data-driven manner, with no ad hoc hyperparameters. The proposed filter is evaluated and compared with a state-of-the-art wavelet-based filter, on the PhysioNet QT Database. The performance is evaluated by measuring the signal-to-noise ratio (SNR) improvement of the filter at SNR levels ranging from -5 to 30dB, in 5dB steps, using additive noise. For a clinical evaluation, the error between the estimated QT-intervals of the original and filtered signals is measured and compared with the benchmark filter. Results: It is shown that the proposed GP filter outperforms the benchmark filter for all the tested noise levels. It also outperforms the state-of-the-art filter in terms of QT-interval estimation error bias and variance. Conclusion: The proposed GP filter is a versatile technique for preprocessing the ECG in clinical and research applications, is applicable to ECG of arbitrary lengths and sampling frequencies, and provides confidence intervals for its performance.

翻译：目的：基于高斯过程的滤器已有效应用于包括心电图滤波在内的多种场景，但该类滤器计算成本高且其超参数选择通常依赖经验。方法：我们开发了一种数据驱动的高斯过程滤器，通过引入心电相位域概念（将心拍在固定采样点数上对齐R峰的时域扭曲表示）来解决上述问题，并假设该相位域服从高斯分布。在该假设下，样本均值与协方差矩阵的计算得以简化，从而无需经验性超参数即可实现数据驱动的高斯过程滤器高效部署。在PhysioNet QT数据库中，将所提滤器与当前最优的小波滤波方法进行对比评估，通过叠加噪声在-5至30dB范围（步长5dB）测量信噪比改善程度。临床评估中，测量原始与滤波信号QT间期估计误差，并与基准滤器比较。结果：在所有测试噪声水平下，所提高斯过程滤器均优于基准滤波器；同时在QT间期估计误差的偏差与方差指标上亦优于现有最优方法。结论：所提高斯过程滤器可作为临床与科研中心电信号预处理的通用技术，适用于任意长度与采样频率的心电信号，并能提供其性能的置信区间。