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

arXiv: https://arxiv.org/abs/2606.30156 · HTML: https://mlsanity.com/paper/2606.30156/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 7 of 7)

- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [DDSP: Differentiable Digital Signal Processing](https://mlsanity.com/paper/2001.04643/) (2020)
- [TROIKA: A General Framework for Heart Rate Monitoring Using Wrist-Type Photoplethysmographic Signals During Intensive Physical Exercise](https://mlsanity.com/paper/1409.5181/) (2014)
- [KID-PPG: Knowledge Informed Deep Learning for Extracting Heart Rate from a Smartwatch](https://mlsanity.com/paper/2405.09559/) (2024)
- [EnhancePPG: Improving PPG-based Heart Rate Estimation with Self-Supervision and Augmentation](https://mlsanity.com/paper/2412.17860/) (2024)
- [Robust CNN-based Respiration Rate Estimation for Smartwatch PPG and IMU](https://mlsanity.com/paper/2401.05469/) (2024)

## Abstract (arXiv)

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.