  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.
