NMCSE: Noise-Robust Multi-Modal Coupling Signal Estimation Method via Optimal Transport for Cardiovascular Disease Detection

The coupling signal refers to a latent physiological signal that characterizes the transformation from cardiac electrical excitation, captured by the electrocardiogram (ECG), to mechanical contraction, recorded by the phonocardiogram (PCG). By encoding the temporal and functional interplay between electrophysiological and hemodynamic events, it serves as an intrinsic link between modalities and offers a unified representation of cardiac function, with strong potential to enhance multi-modal cardiovascular disease (CVD) detection. However, existing coupling signal estimation methods remain highly vulnerable to noise, particularly in real-world clinical and physiological settings, which undermines their robustness and limits practical value. In this study, we propose Noise-Robust Multi-Modal Coupling Signal Estimation (NMCSE), which reformulates coupling signal estimation as a distribution matching problem solved via optimal transport. By jointly aligning amplitude and timing, NMCSE avoids noise amplification and enables stable signal estimation. When integrated into a Temporal-Spatial Feature Extraction (TSFE) network, the estimated coupling signal effectively enhances multi-modal fusion for more accurate CVD detection. To evaluate robustness under real-world conditions, we design two complementary experiments targeting distinct sources of noise. The first uses the PhysioNet 2016 dataset with simulated hospital noise to assess the resilience of NMCSE to clinical interference. The second leverages the EPHNOGRAM dataset with motion-induced physiological noise to evaluate intra-state estimation stability across activity levels. Experimental results show that NMCSE consistently outperforms existing methods under both clinical and physiological noise, highlighting it as a noise-robust estimation approach that enables reliable multi-modal cardiac detection in real-world conditions.