Uncertainty-quantified Pulse Signal Recovery from Facial Video using Regularized Stochastic Interpolants

1. Problem Statement

Imaging Photoplethysmography (iPPG) is a non-contact technique that recovers a human's blood volume pulse (BVP) waveform from facial video using standard RGB cameras. While current state-of-the-art (SOTA) algorithms achieve high accuracy on benchmark datasets, they suffer from a critical limitation: they lack uncertainty quantification (UQ).

• The Gap: Existing methods (both traditional signal processing and deep learning) typically output a single "point estimate" of the pulse signal. They do not sample the solution space to determine the confidence or reliability of that estimate.
• Clinical Need: For clinical adoption, doctors require not just a heart rate number, but an understanding of the model's reliability (e.g., "Is this reading trustworthy given the patient's skin tone or motion artifacts?").
• The Challenge: The mapping from camera pixel intensity to the ground-truth BVP signal is a complex, ill-posed inverse problem involving non-linear noise, motion artifacts, specular reflections, and varying skin tones. Traditional regularized optimization approaches often fail to model this stochasticity effectively.

2. Methodology: RIS-iPPG

The authors propose RIS-iPPG (Regularized Interpolants with Stochasticity for iPPG), a framework based on Stochastic Interpolants and Flow-based Diffusion Models.

A. Core Framework: Stochastic Interpolants

Instead of learning a deterministic mapping, the authors model the recovery as a stochastic process that transforms the distribution of camera pixel signals ($p_0$) into the distribution of ground-truth BVP signals ($p_1$).

• Interpolant Definition: They define a time-dependent stochastic process $x_t$ that smoothly interpolates between a sample from the camera distribution ($x_0$) and the ground truth ($x_1$) over time $t \in [0, 1]$:
  $$x_t = (1-t)x_0 + tx_1 + \sqrt{2t(1-t)}z$$
  where $z$ is Gaussian noise.
• Learning Flow and Score: The goal is to learn two neural networks:
  1. Flow Vector ($v_\theta$): Predicts the instantaneous velocity (drift) of the distribution.
  2. Score Vector ($s_\theta$): Predicts the gradient of the log-density (related to a denoiser).
• Inference (Test-Time Sampling): At test time, the system starts with the camera measurement as the initial condition and solves a Stochastic Differential Equation (SDE) in reverse. By sampling this SDE $N$ times, the model generates multiple plausible BVP waveforms, allowing for the construction of a posterior distribution and uncertainty estimates.

B. Regularization: Residual Correlation Loss (RCL)

The authors observed that unregularized flow models struggle with temporal consistency, especially under motion noise. Since physiological changes are slowly varying, the error in flow predictions should be consistent across adjacent time windows.

• Concept: For two overlapping, adjacent time windows, the residual vectors (difference between predicted flow and ground-truth flow) should point in the same direction.
• Loss Function: They introduce the Residual Correlation Loss (RCL), which maximizes the Pearson correlation between the residual vectors of adjacent windows.
  $$L_{RCL} = 1 - \text{Correlation}(p, q)$$
  where $p$ and $q$ are the residual vectors for the two windows.
• Effect: This acts as a temporal smoothness prior, forcing the model to learn physically plausible, consistent flow fields, which improves the capture of signal modes and reduces spurious uncertainty.

3. Key Contributions

1. First Posterior Sampling Framework for iPPG: The paper introduces the first method to treat iPPG recovery as a posterior sampling problem using flow-based diffusion models, enabling the generation of multiple solution realizations rather than a single point estimate.
2. Residual Correlation Loss (RCL): A novel regularization technique that enforces temporal consistency in the learned flow vectors. The authors demonstrate that this significantly improves signal recovery quality and the ability to capture multimodal distributions (e.g., distinguishing between noise peaks and true heart rate peaks).
3. Uncertainty Quantification (UQ) Baselines: The study establishes the first baselines for UQ in iPPG, evaluating not just accuracy but also calibration and reliability across protected attributes (skin tone and gender).
4. Comprehensive Evaluation: Extensive testing on three datasets (MMSE-HR, PURE, UBFC-rPPG) showing competitive or SOTA performance in heart rate estimation while providing critical uncertainty metrics.

4. Experimental Results

The method was evaluated on three standard datasets: MMSE-HR, PURE, and UBFC-rPPG.

• Heart Rate Estimation Accuracy:
  • RIS-iPPG achieved State-of-the-Art (SOTA) performance on the PURE dataset (MAE: 0.38 bpm, RMSE: 1.28 bpm).
  • It achieved highly competitive results on MMSE-HR (MAE: 1.97 bpm) and UBFC-rPPG (MAE: 0.47 bpm), comparable to or better than existing supervised and unsupervised methods.
• Spectrum Estimation:
  • The inclusion of RCL loss improved spectrum estimation accuracy (lower RMSE, higher Pearson Correlation) compared to the unregularized model.
  • Qualitative results (Figure 3) show that RCL helps the model correctly identify the true heart rate peak while maintaining appropriate uncertainty around noise peaks, whereas the unregularized model often smoothed out the spectrum or predicted incorrect modes.
• Uncertainty Quantification:
  • Calibration: The model demonstrated good calibration curves, meaning the predicted confidence intervals aligned well with observed error rates.
  • Protected Attributes: The authors analyzed performance across skin tones and gender. While accuracy was slightly lower for darker skin tones (a known challenge in iPPG), the uncertainty estimates were well-calibrated for all groups. This means the model correctly identified when it was less certain about darker skin tones, a crucial feature for clinical safety.
• Ablation Studies:
  • Removing RCL led to higher variance in predictions and failure to capture multimodal distributions.
  • Conditioning on raw video color channels as guidance signals actually degraded performance, validating the choice to rely on temporal regularization instead.

5. Significance and Impact

• Clinical Trust: By providing uncertainty estimates, RIS-iPPG addresses a major barrier to the clinical adoption of AI in healthcare. Clinicians can now see not just the predicted heart rate, but also the "confidence" of that prediction, allowing them to make better-informed decisions.
• Robustness: The RCL regularization makes the model more robust to motion artifacts and out-of-distribution noise, which are common in real-world scenarios.
• Fairness: The explicit evaluation and calibration of uncertainty across protected attributes (skin tone, gender) set a new standard for fairness and reliability in medical AI, ensuring that the model's limitations are transparent to the user.
• Paradigm Shift: The paper shifts the iPPG paradigm from "denoising to a single point" to "sampling a probability distribution," opening the door for more sophisticated probabilistic reasoning in remote physiological monitoring.

In conclusion, RIS-iPPG represents a significant advancement in non-contact vital sign monitoring by combining the generative power of stochastic interpolants with a novel temporal regularization strategy to deliver both high-accuracy heart rate estimation and clinically vital uncertainty quantification.