Wrist-worn photoplethysmography (PPG) enables continuous monitoring of cardiopulmonary physiology, but reliable heart rate (HR) and respiratory rate (RR) estimation in free-living conditions remains challenging due to non-stationary motion artifacts that spectrally overlap with physiological dynamics. Existing signal-processing methods degrade under strong motion, while unconstrained deep learning approaches often lack physiological interpretability and identifiable structure. We propose a Physically-Constrained Harmonic Separation (PCHS) framework that formulates HR and RR estimation from wrist PPG as an analysis-by-synthesis problem, where accelerometer measurements condition artifact separation rather than directly regressing vital signs. A physics-guided harmonic generator decomposes the observed signal into quasi-periodic physiological components and a motion-related residual, enabling HR recovery from the fundamental frequency and RR prediction from respiratory-driven modulations of the harmonic parameters. Robust reconstruction objectives, separation constraints, and uncertainty-aware weighting stabilize the decomposition under motion. Experiments on the motion-intensive PPG-DaLiA dataset demonstrate that PCHS outperforms state-of-the-art methods while yielding interpretable signal decompositions that effectively disentangle physiological activity from motion artifacts.
Respiratory rate is a vital indicator of pulmonary and cardiovascular health, yet conventional methods for estimating respiratory rate are often intrusive due to their contact-based nature. Remote photoplethysmography offers a promising non-contact alternative and has been widely used for heart rate estimation; however, its potential for respiratory rate estimation remains underexplored. Existing methods typically adapt green and chrominance-based projections originally designed for heart rate estimation, which only partially capture respiratory dynamics. Most prior work focuses on the Eulerian representation with fixed or empirically selected RGB projections. To address these gaps, we propose a skin-tone-aware dynamic RGB signal projection that captures respiratory information. To mitigate the sensitivity of the Lagrangian representation to non-respiratory motion, we introduce a denoising network for motion-based remote photoplethysmography signals. We further design a phase-independent contrastive loss that enables Eulerian and Lagrangian representations to collaboratively learn respiratory rate information. We also introduce RR-rPPG, a respiratory-rate facial video dataset with Indian demographic representation. We evaluate the method on RR-rPPG and the publicly available COHFACE dataset, where it consistently outperforms comparison methods and achieves up to a 42.1% reduction in mean absolute error across the evaluated settings. The proposed framework demonstrates the effectiveness of jointly leveraging skin-tone-aware Eulerian and denoised Lagrangian representations for contactless respiratory rate estimation from facial videos. In addition, RR-rPPG contributes a diverse benchmark resource for future research in remote respiratory monitoring. The code and dataset will be made publicly available upon paper acceptance.