Physically-Constrained Harmonic Separation for Robust Heart and Respiratory Rate Estimation from Wrist Photoplethysmography

Reliable heart rate (HR) and respiratory rate (RR) estimation from wrist-worn photoplethysmography (PPG) is frequently compromised by motion artifacts that overlap with physiological signals. Existing deep learning methods often treat this as a black-box regression problem, which can lead to reliance on spurious correlations rather than true physiological dynamics. This paper asks whether explicitly modeling the physics of PPG signal generation can improve robustness and interpretability in free-living conditions.

The authors propose the Physically-Constrained Harmonic Separation (PCHS) framework. Instead of direct regression, PCHS treats signal processing as an analysis-by-synthesis problem. It uses a dual-stream encoder where accelerometer data conditions the PPG representation via feature-wise linear modulation (FiLM). A physics-informed decoder then synthesizes a pulse-synchronous physiological signal using a harmonic model, while an additive residual branch captures non-harmonic motion artifacts. The model also predicts a time-varying uncertainty estimate to downweight segments where motion corruption is too severe for reliable inference.

PCHS outperforms state-of-the-art signal processing and deep learning methods on the motion-intensive PPG-DaLiA dataset, achieving a mean absolute error of 3.20 bpm for heart rate. The framework provides interpretable signal decompositions, effectively isolating cardiac structure from motion-induced noise. Ablation studies confirm that the combination of harmonic synthesis, motion-aware conditioning, and uncertainty-based inference is essential for maintaining accuracy under high-motion conditions.

By moving away from black-box regression toward physiology-informed generative modeling, this approach provides a more robust way to handle the non-stationary motion artifacts inherent in wearable sensing. The interpretability of the decomposed signals allows for better validation of the model's internal logic, making it a promising step toward reliable, continuous health monitoring in daily life.