# Recovering Pulse Waves from Video Using Deep Unrolling and Deep Equilibrium Models

arXiv: https://arxiv.org/abs/2503.17269 · HTML: https://mlsanity.com/paper/2503.17269/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 93 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 30 of 40)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [TSM: Temporal Shift Module for Efficient Video Understanding](https://mlsanity.com/paper/1811.08383/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [DeepPhys: Video-Based Physiological Measurement Using Convolutional Attention Networks](https://mlsanity.com/paper/1805.07888/) (2018)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [Multi-Task Temporal Shift Attention Networks for On-Device Contactless Vitals Measurement](https://mlsanity.com/paper/2006.03790/) (2020)
- [Remote Photoplethysmograph Signal Measurement from Facial Videos Using Spatio-Temporal Networks](https://mlsanity.com/paper/1905.02419/) (2019)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [PhysFormer: Facial Video-based Physiological Measurement with Temporal Difference Transformer](https://mlsanity.com/paper/2111.12082/) (2021)
- [Monotone operator equilibrium networks](https://mlsanity.com/paper/2006.08591/) (2020)
- [LUVLi Face Alignment: Estimating Landmarks' Location, Uncertainty, and Visibility Likelihood](https://mlsanity.com/paper/2004.02980/) (2020)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [Video-based Remote Physiological Measurement via Cross-verified Feature Disentangling](https://mlsanity.com/paper/2007.08213/) (2020)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [EfficientPhys: Enabling Simple, Fast and Accurate Camera-Based Vitals Measurement](https://mlsanity.com/paper/2110.04447/) (2021)
- [Stabilizing Equilibrium Models by Jacobian Regularization](https://mlsanity.com/paper/2106.14342/) (2021)
- [The Way to my Heart is through Contrastive Learning: Remote Photoplethysmography from Unlabelled Video](https://mlsanity.com/paper/2111.09748/) (2021)
- [Deep Equilibrium Optical Flow Estimation](https://mlsanity.com/paper/2204.08442/) (2022)
- [rPPG-Toolbox: Deep Remote PPG Toolbox](https://mlsanity.com/paper/2210.00716/) (2022)
- [PulseGAN: Learning to generate realistic pulse waveforms in remote photoplethysmography](https://mlsanity.com/paper/2006.02699/) (2020)
- [Meta-rPPG: Remote Heart Rate Estimation Using a Transductive Meta-Learner](https://mlsanity.com/paper/2007.06786/) (2020)
- [Camera Measurement of Physiological Vital Signs](https://mlsanity.com/paper/2111.11547/) (2021)
- [FaceBoxes: A CPU Real-time Face Detector with High Accuracy](https://mlsanity.com/paper/1708.05234/) (2017)
- [Deep Equilibrium Approaches to Diffusion Models](https://mlsanity.com/paper/2210.12867/) (2022)
- [AutoHR: A Strong End-to-end Baseline for Remote Heart Rate Measurement with Neural Searching](https://mlsanity.com/paper/2004.12292/) (2020)
- [rPPG-MAE: Self-supervised Pre-training with Masked Autoencoders for Remote Physiological Measurement](https://mlsanity.com/paper/2306.02301/) (2023)
- [Contrast-Phys+: Unsupervised and Weakly-supervised Video-based Remote Physiological Measurement via Spatiotemporal Contrast](https://mlsanity.com/paper/2309.06924/) (2023)
- [Neuron Structure Modeling for Generalizable Remote Physiological Measurement](https://mlsanity.com/paper/2303.05955/) (2023)
- [Recurrence without Recurrence: Stable Video Landmark Detection with Deep Equilibrium Models](https://mlsanity.com/paper/2304.00600/) (2023)

## Built on by (most cited first, 2 of 2)

- [Expressive Power of Implicit Models: Rich Equilibria and Test-Time Scaling](https://mlsanity.com/paper/2510.03638/) (2025)
- [Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach](https://mlsanity.com/paper/2602.03297/) (2026)

## Abstract (arXiv)

Camera-based monitoring of vital signs, also known as imaging photoplethysmography (iPPG), has seen applications in driver-monitoring, perfusion assessment in surgical settings, affective computing, and more. iPPG involves sensing the underlying cardiac pulse from video of the skin and estimating vital signs such as the heart rate or a full pulse waveform. Some previous iPPG methods impose model-based sparse priors on the pulse signals and use iterative optimization for pulse wave recovery, while others use end-to-end black-box deep learning methods. In contrast, we introduce methods that combine signal processing and deep learning methods in an inverse problem framework. Our methods estimate the underlying pulse signal and heart rate from facial video by learning deep-network-based denoising operators that leverage deep algorithm unfolding and deep equilibrium models. Experiments show that our methods can denoise an acquired signal from the face and infer the correct underlying pulse rate, achieving state-of-the-art heart rate estimation performance on well-known benchmarks, all with less than one-fifth the number of learnable parameters as the closest competing method.