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Bayesian ECG reconstruction using denoising diffusion generative models

Gabriel V. Cardoso, Lisa Bedin, Josselin Duchateau, Rémi Dubois, Eric Moulines

TL;DR

This work develops a denoising diffusion generative model (DDGM) trained exclusively on healthy, multi-lead ECG data to capture precise morphology and inter-lead dependencies. The authors introduce ECGDiff, a diffusion-based generator with a VE forward process and a learned backward denoiser, capable of producing a single healthy heartbeat conditioned on patient attributes and RR interval, across nine leads. They showcase the DDGM as a versatile prior for linear inverse ECG problems via posterior sampling (SMC), enabling denoising, missing-lead reconstruction, QT estimation, and anomaly detection without additional retraining, while providing interpretable, white-box diagnostics. The approach yields realistic ECG generation, reliable reconstruction performance (e.g., missing-lead recovery) and robust QT–RR modeling, with practical implications for clinical monitoring and patient-specific cardiac assessment.

Abstract

In this work, we propose a denoising diffusion generative model (DDGM) trained with healthy electrocardiogram (ECG) data that focuses on ECG morphology and inter-lead dependence. Our results show that this innovative generative model can successfully generate realistic ECG signals. Furthermore, we explore the application of recent breakthroughs in solving linear inverse Bayesian problems using DDGM. This approach enables the development of several important clinical tools. These include the calculation of corrected QT intervals (QTc), effective noise suppression of ECG signals, recovery of missing ECG leads, and identification of anomalous readings, enabling significant advances in cardiac health monitoring and diagnosis.

Bayesian ECG reconstruction using denoising diffusion generative models

TL;DR

This work develops a denoising diffusion generative model (DDGM) trained exclusively on healthy, multi-lead ECG data to capture precise morphology and inter-lead dependencies. The authors introduce ECGDiff, a diffusion-based generator with a VE forward process and a learned backward denoiser, capable of producing a single healthy heartbeat conditioned on patient attributes and RR interval, across nine leads. They showcase the DDGM as a versatile prior for linear inverse ECG problems via posterior sampling (SMC), enabling denoising, missing-lead reconstruction, QT estimation, and anomaly detection without additional retraining, while providing interpretable, white-box diagnostics. The approach yields realistic ECG generation, reliable reconstruction performance (e.g., missing-lead recovery) and robust QT–RR modeling, with practical implications for clinical monitoring and patient-specific cardiac assessment.

Abstract

In this work, we propose a denoising diffusion generative model (DDGM) trained with healthy electrocardiogram (ECG) data that focuses on ECG morphology and inter-lead dependence. Our results show that this innovative generative model can successfully generate realistic ECG signals. Furthermore, we explore the application of recent breakthroughs in solving linear inverse Bayesian problems using DDGM. This approach enables the development of several important clinical tools. These include the calculation of corrected QT intervals (QTc), effective noise suppression of ECG signals, recovery of missing ECG leads, and identification of anomalous readings, enabling significant advances in cardiac health monitoring and diagnosis.
Paper Structure (30 sections, 2 theorems, 34 equations, 14 figures, 3 tables)

This paper contains 30 sections, 2 theorems, 34 equations, 14 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Works
  4. Notations
  5. DDGM for ECG
  6. ECG
  7. DDGM
  8. Forward noising process
  9. Backward denoising process
  10. The $\operatorname{ECGDiff}$ generative model
  11. Dataset and preprocessing
  12. Training
  13. Results
  14. DDGM as a prior for ECG reconstruction
  15. Sequential Monte Carlo (SMC)
  16. ...and 15 more sections

Key Result

Lemma 6.1

Let $\sequence{\eta}[k][\mathbb{N}]$ satisfy $\eta_{k}^2 \in [0,{\upsilon}^2_k]$ for all $k \in [1:K]$. Then

Figures (14)

  • Figure 1: Example of single normal beat generated with DDGM, across multiple diffusion steps.
  • Figure 2: EMD of generated ECGs vs. test (dotted) and train (plain), w.r.t diffusion steps. Conditioned (resp. uncond.) DDGM in oragnge (resp. gray). EMD of test (resp. noisy-test) vs. train in red (resp. blue). Error bars correspond to different training batches of size $2864$.
  • Figure 3: Box-plot of uncertainties estimation for train, test, generated (Gen) and MI heart beats.
  • Figure 4: Conditional generation example. Observation: (aVL, aVR, aVF) with $\sigma=0.1$. Red solid/dashed lines: observed/real signal. Shaded zone: observed signal plus $3\times \text{std}$ of the guiding function \ref{['eq:potential_smc']}, std values on top. Blue: posterior samples.
  • Figure 5: Illustration of denoising with Gaussian noise for two different test signals. The original data used to generate the noised observation used to generate the denoised posterior samples is shown in black for illustration purposes.
  • ...and 9 more figures

Theorems & Definitions (4)

  • Lemma 6.1
  • proof
  • Lemma 6.2
  • proof