A Data-Driven Gaussian Process Filter for Electrocardiogram Denoising (2301.02607v2)

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.

• The paper presents a novel data-driven GP filter that automatically computes phase domain statistics for efficient ECG denoising.
• It demonstrates significant improvements in SNR and reduced QT-interval estimation error compared to wavelet-based benchmarks.
• The method eliminates manual hyperparameter tuning, enabling robust, real-time processing of diverse ECG signals.

A Data-Driven Gaussian Process Filter for Electrocardiogram Denoising

Introduction

The paper "A Data-Driven Gaussian Process Filter for Electrocardiogram Denoising" (2301.02607) presents a novel approach to electrocardiogram (ECG) denoising using Gaussian Processes (GP). While GP-based filters have previously found utility in ECG processing, they often involve significant computational demands and require ad hoc selection of hyperparameters. This work aims to mitigate these challenges by leveraging a data-driven approach that eschews arbitrary parameter setting and facilitates efficient computation.

Methodology

At the core of this study is the development of a data-driven GP filter utilizing the ECG phase domain—a transformation that aligns ECG beats in a time-warped representation, standardizing their sampling and aligning R-peaks. This innovative use of the phase domain enables the simple computation of the necessary sample mean and covariance matrices, simplifying the implementation of the GP filter without manually setting hyperparameters.

The proposed method models ECG measurements $x(t)$ as noisy versions of clean ECG signals $s(t)$, manipulated with Gaussian noise. The transformation into the phase domain allows the derivation of statistical parameters from ECG beats, effectively modeling them as samples from an underlying Gaussian distribution. These phase-domain parameters are then mapped back to the time domain to facilitate noise reduction through Bayesian inference.

Metrics of signal quality, namely the signal-to-noise ratio (SNR) and QT-interval estimation error, are employed to evaluate the filter's performance against a state-of-the-art wavelet-based benchmark. Notably, both categorical improvements in mean SNR and reductions in estimation error variance underscore the efficacy of this data-driven approach.

Results

The data-driven GP filter consistently outperforms the benchmark wavelet denoiser. Numerical evaluation reveals that, across all noise levels from -5 dB to 30 dB, the proposed filter enhances SNR more effectively. In clinical terms, it also lowers the error bias and variance in QT-interval estimation, a critical ECG diagnostic parameter. These improvements suggest a robust alternative methodology for ECG noise attenuation applicable across various noise environments.

Discussion

The study highlights the potential for GP-based denoising without resorting to the computationally intensive covariance matrix inversions typically seen in conventional GP implementations. Instead, it leverages phase domain statistics to make real-time applications feasible, even for long ECG records. By dismissing the ad hoc assumptions conventionally associated with GP model hyperparameters, this approach supports a broader range of ECG applications, inclusive of diverse sampling frequencies and signal lengths.

The ramifications of this research are twofold: It establishes a flexible and efficient denoising mechanism for ECG data, and it lays groundwork for further exploration into probabilistic models of physiological signals. Future iterations of this work could relax the assumptions on underlying Gaussian distributions or refine techniques for R-peak detection, thus improving the efficacy of handle morphological variations in heartbeats.

Conclusion

The data-driven GP filter represents a significant step forward in ECG preprocessing techniques, offering a method that is not only computationally efficient but also free from the constraints of arbitrary parameter selection. It paves the way for enhanced accuracy in ECG signal analyses, pivotal in both clinical diagnostics and research applications. Continued refinements and adjustments to this model could yield even greater advances in handling cardiac electrophysiological data.