Interaction-Gated Time-Frequency Learning for Parameter-Efficient PPG-Based Heart Rate Estimation

Introduction

Photoplethysmography (PPG) is a popular, low‑cost way to monitor heart rate, but its signals are easily corrupted by motion, ambient light, and individual physiological differences. Traditional approaches either focus on the raw waveform (temporal domain) or on its periodicity (frequency domain), often requiring large neural networks to achieve acceptable accuracy. The recent TF‑IG framework tackles this trade‑off by explicitly learning from both domains in a compact architecture, achieving high‑precision heart‑rate estimates with fewer than 100 K parameters.

Dual‑Branch Architecture: Temporal and Frequency Streams

TF‑IG processes the PPG signal through two parallel branches. The temporal branch uses dilated depthwise‑separable convolutions to capture fine‑grained pulse morphology while keeping the parameter count low. Dilations expand the receptive field without adding weights, allowing the network to model long‑range dependencies such as the systolic‑diastolic pattern. The frequency branch converts the signal into a bounded log‑spectrogram, preserving the cardiac periodicity that is often more robust to noise. A lightweight convolutional stack extracts spectral features that highlight the dominant heart‑beat frequency.

Interaction‑Gated Fusion

The novelty of TF‑IG lies in its interaction‑gated fusion module. Rather than simply concatenating or adding the two feature maps, the module computes a pairwise agreement score between temporal and spectral representations. This score gates the contribution of each branch on a per‑feature basis, allowing the network to emphasize the domain that is more reliable for a given segment (e.g., relying on spectral cues during motion artifacts). The gated features are then merged and passed to a shared regression head, which predicts the final beats‑per‑minute (BPM) value.

Parameter‑Efficient Regression Head

A single regression head, shared across the fused and individual branch outputs, maps the combined representation to a scalar heart‑rate estimate. Sharing parameters reduces redundancy and further curtails model size, making TF‑IG suitable for deployment on wearable devices with limited memory and compute budgets.

Performance Highlights

Evaluated on the BIDMC PPG and Respiration Dataset with a strict subject‑exclusive split, TF‑IG achieves:

• Mean Absolute Error (MAE): 1.23 BPM
• Root Mean Square Error (RMSE): 2.06 BPM
• Pearson correlation: 0.9934
• 92.3 % of predictions within 3 BPM

All of this is delivered with only 84.6 K trainable parameters, a stark contrast to many state‑of‑the‑art models that exceed several hundred thousand parameters.

Why Interaction Matters

Ablation studies show that removing the interaction‑gated fusion degrades accuracy noticeably, confirming that the explicit modeling of cross‑domain agreement is essential. Likewise, disabling either the temporal or frequency branch reduces performance, underscoring the complementary nature of morphology‑ and periodicity‑based cues.

Practical Implications

The TF‑IG design aligns well with the constraints of modern wearables:

• Low memory footprint enables on‑device inference without offloading to the cloud.
• Robustness to noise improves reliability in everyday activities such as exercise or daily chores.
• Scalable training benefits from the parameter‑efficient architecture, allowing rapid iteration on new datasets or sensor modalities.

Closing Thoughts

By marrying lightweight temporal convolutions with a concise spectral extractor and a smart interaction‑gated fusion, TF‑IG demonstrates that high‑accuracy heart‑rate estimation does not require heavyweight models. This approach opens the door for more energy‑efficient, real‑time health monitoring solutions that can run directly on the limited hardware of consumer wearables.