Uncertainty-Aware PPG-2-ECG for Enhanced Cardiovascular Diagnosis using Diffusion Models

TL;DR

Uncertainty in recovering ECG signals from PPG signals is addressed with UA-P2E, a conditional diffusion framework that samples multiple ECG candidates from the posterior $\hat{\pi}(X|Y)$. It introduces an Expected Score Classifier (ESC) that optimally aggregates classification scores across posterior ECG samples, with theoretical proofs under a posterior-sampling assumption. The method is validated on the MIMIC-III and CinC datasets, showing improved conversion quality (lower RMSE and FD) and better cardiovascular condition detection (higher AUROC and favorable risk-coverage) compared to single-sample baselines. Visualization strategies are provided to present multiple ECG candidates to clinicians, enhancing interpretability while accounting for uncertainty.

Abstract

Analyzing the cardiovascular system condition via Electrocardiography (ECG) is a common and highly effective approach, and it has been practiced and perfected over many decades. ECG sensing is non-invasive and relatively easy to acquire, and yet it is still cumbersome for holter monitoring tests that may span over hours and even days. A possible alternative in this context is Photoplethysmography (PPG): An optically-based signal that measures blood volume fluctuations, as typically sensed by conventional ``wearable devices''. While PPG presents clear advantages in acquisition, convenience, and cost-effectiveness, ECG provides more comprehensive information, allowing for a more precise detection of heart conditions. This implies that a conversion from PPG to ECG, as recently discussed in the literature, inherently involves an unavoidable level of uncertainty. In this paper we introduce a novel methodology for addressing the PPG-2-ECG conversion, and offer an enhanced classification of cardiovascular conditions using the given PPG, all while taking into account the uncertainties arising from the conversion process. We provide a mathematical justification for our proposed computational approach, and present empirical studies demonstrating its superior performance compared to state-of-the-art baseline methods.

Figures (10)

• Figure 1: Illustration of our proposed UA-P2E for PPG-2-ECG conversion-classification framework.
• Figure 2: MIMIC-III Results: Diffusion-based multiple solutions in the temporal domain. Each temporal point displays an interval containing 95% of our ECG/PPG synthetic values. The top row depicts the ECG solution cloud (GREEN) resulting from the PPG-2-ECG conversion, while the bottom row shows the PPG solution cloud (RED) from the reverse conversion of ECG-2-PPG.
• Figure 3: CinC Results: ROC curves for the classification performance of various strategies (see Appendix \ref{['app: Classification Strategies']}). Higher curves indicate better performance.
• Figure 4: CinC Results: Risk-Coverage curves for the uncertainty quantification performance of various strategies (see Appendix \ref{['app: Classification Strategies']}). Lower curves indicate better performance.
• Figure 5: CinC Results: Empirical evidence of inherent uncertainty in the PPG-2-ECG conversion-classification framework. (a) The conversion spread and variability as proposed by belhasin2023principal. High reconstruction error with many PCs indicates high uncertainty in terms of spread and variability. (b) Classification uncertainty shows relatively small interval sizes of ECG probability scores for each PPG (right), which can be effectively modeled using just 100 ECG samples (left).

Theorems & Definitions (4)

• Definition 3.1: Single Score Classifier
• Definition 3.2: Expected Score Classifier
• Theorem 3.1: Optimality of the Expected Score Classifier
• Theorem