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A Data-Driven Gaussian Process Filter for Electrocardiogram Denoising

Mircea Dumitru, Qiao Li, Erick Andres Perez Alday, Ali Bahrami Rad, Gari D. Clifford, Reza Sameni

TL;DR

The paper tackles ECG denoising by reformulating Gaussian-process filtering in a data-driven, phase-domain framework, eliminating ad hoc hyperparameters and enabling efficient beat-wise processing for long ECG records. By projecting beats into a phase domain, beats are treated as samples from a common GP, with phase-domain statistics used to compute a time-domain posterior mean without expensive inversions, especially in the diagonal covariance variant. The method outperforms a state-of-the-art wavelet denoiser in SNR enhancement and yields more accurate QT-interval estimates, while providing uncertainty quantification through posterior variances. Practically, the approach supports ECG preprocessing for clinical and research uses across arbitrary lengths and sampling rates, and includes tools for synthetic ECG generation from learned parameters for data augmentation.

Abstract

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.

A Data-Driven Gaussian Process Filter for Electrocardiogram Denoising

TL;DR

The paper tackles ECG denoising by reformulating Gaussian-process filtering in a data-driven, phase-domain framework, eliminating ad hoc hyperparameters and enabling efficient beat-wise processing for long ECG records. By projecting beats into a phase domain, beats are treated as samples from a common GP, with phase-domain statistics used to compute a time-domain posterior mean without expensive inversions, especially in the diagonal covariance variant. The method outperforms a state-of-the-art wavelet denoiser in SNR enhancement and yields more accurate QT-interval estimates, while providing uncertainty quantification through posterior variances. Practically, the approach supports ECG preprocessing for clinical and research uses across arbitrary lengths and sampling rates, and includes tools for synthetic ECG generation from learned parameters for data augmentation.

Abstract

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.
Paper Structure (14 sections, 13 equations, 5 figures, 1 algorithm)

This paper contains 14 sections, 13 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Gaussian process-based ECG filtering
  3. The mathematical model
  4. The GP filter with diagonal covariance matrix
  5. Computational cost and model selection
  6. Hyperparameter selection
  7. Results
  8. Baseline wander removal
  9. R-peak detection and heartbeat segmentation
  10. Evaluation
  11. SNR improvement performance
  12. Clinical parameters preservation
  13. Discussion and conclusion
  14. Acknowledgements

Figures (5)

  • Figure 1: Time-domain measurements beats (top) and the corresponding phase domain ECG beats (bottom), with the same number $\mathcal{T}$ of samples for the first 6 beats of sel100 record from QTDB Laguna1997 with $0$ dB Gaussian additive noise. Transformation matrices $\bm{\Theta}_{i}$ are defined via \ref{['eeq:2bis']}.
  • Figure 2: Corner detail example of transformation matrix $\bm{\Theta}_{i}$ (left), $\bm{\Theta}_{i}^{T}$ (middle) and the corresponding (diagonal) Gramian $\bm{G}_{i} = \bm{\Theta}_{i}^{T} \bm{\Theta}_{i}$ (right).
  • Figure 3: The sel100 recording from the PhysioNet QTDB Laguna1997. From top to bottom the measurements $\bm{x}$ vs. the prior estimate \ref{['eeq:10']}, the posterior estimate \ref{['eeq:11']}, and the wavelet denoiser (Section \ref{['subsec:evaluation']}), at different input SNR levels. The post-filtering SNR improvement is noted in each case.
  • Figure 4: Mean and standard deviation SNR improvement using the proposed $\mathcal{G}\mathcal{P}$ filter and the benchmark wavelet denoiser Sameni2017 across all samples of the PhysioNet QTDB Laguna1997, in leads I and II, with 5 repetitions using different noise instances per record.
  • Figure 5: The median and the interquartile range for $\Delta$QT estimations corresponding to the proposed and benchmark filters across all samples of the PhysioNet QTDB Laguna1997.