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

Anh Khoi Pham, Phat Lam, Thien Truong Nguyen Ly, Lam Pham

arXiv:2610.28693v1cs.LGcs.AIeess.SP

TL;DR

PPG enables low-cost, non-invasive HR monitoring, but waveform distortion and physiological and measurement variability make reliable estimation challenging. TF-IG combines temporal and spectral representations through interaction-gated fusion and shared prediction; on the subject-exclusive BIDMC split, it reports strong estimation metrics with a compact parameter footprint.

  • Problem

    PPG-based HR estimation is challenging because waveform measurements are affected by physiological and acquisition factors, while effective integration of complementary temporal and spectral evidence remains a design problem.

    Source: §1 · p. 2

  • Method

    TF-IG combines temporal and bounded log-spectrogram branches with interaction-gated fusion and a parameter-shared regression head for HR prediction.

    Source: §1 · pp. 2–3

  • Results

    On the subject-exclusive BIDMC split, TF-IG achieves an MAE of 1.227 BPM, an RMSE of 2.060 BPM, a Pearson correlation of 0.9934, and a CP3 of 92.28%.

    Source: §1 · p. 3, §5 · p. 12

  • Takeaways & Limitations

    Ablations validate the complementary roles of dual-domain representation learning, interaction-gated fusion, and shared regression in estimation performance.

    Source: §1 · p. 3, §5 · p. 12

Abstract

from arXiv · show

Photoplethysmography (PPG) enables low-cost and non-invasive heart rate (HR) monitoring but remains sensitive to waveform distortion, physiological variability, and measurement interference. Temporal waveform characteristics and frequency-domain periodicity provide complementary information for HR estimation; however, effectively exploring and integrating these representations within a compact model remains challenging. This paper proposes TF-IG, a parameter-efficient interaction-gated time-frequency learning framework for PPG-based HR estimation. TF-IG employs a dual-branch architecture in which a temporal branch captures pulse morphology via dilated depthwise-separable convolutions, while a frequency branch extracts cardiac periodicity information from bounded log-spectrogram representations. To combine the two domains, we introduce an interaction-gated fusion module that explicitly models feature agreement and discrepancy, while also learning feature-wise weights to balance temporal and spectral information. A parameter-shared regression head further maps the temporal, spectral, and fused representations into the final HR prediction space. Experiments on the benchmark BIDMC PPG and Respiration Dataset using a subject-exclusive training, validation, and test protocol show that TF-IG achieves a mean absolute error (MAE) of 1.227 BPM, a root mean square error (RMSE) of 2.060 BPM, a Pearson correlation coefficient of 0.9934, and 92.28 percent of estimates within 3 BPM, while remaining parameter-efficient with only 84.6K parameters. Ablation results further demonstrate the complementary contributions of the temporal and frequency branches, interaction-gated fusion, and shared regression head. These results indicate that explicitly modeling cross-domain interactions provides an effective accuracy-complexity trade-off for lightweight PPG-based HR estimation.

1 Introduction

PPG offers low-cost, non-invasive continuous HR sensing, yet waveform and acquisition variability challenge reliable estimation. TF-IG addresses the challenge of combining temporal and spectral evidence with interaction-gated fusion and shared prediction.

1 Introduction

  • PPG provides compact, wearable sensing, but physiological and acquisition factors can distort its waveform and challenge reliable HR estimation.Continuous HR monitoring also serves clinical observation, fitness assessment, ambulatory healthcare, and long-term monitoring.Source: §1 · pp. 1–2
  • Temporal morphology and spectral periodicity offer complementary HR evidence, but their interaction remains a design challenge when signals provide partly consistent and partly different evidence.Prior work has demonstrated the utility of signal, spectral, and time-frequency representations, but their availability alone does not determine how to combine them.Source: §1 · p. 2
  • TF-IG pairs dilated depthwise-separable temporal convolutions and attention pooling with bounded log-spectrogram features, interaction-gated fusion, and a shared HR regression head.The fusion models co-activation and discrepancy through element-wise multiplication and absolute difference, while feature-wise gates balance the domains.Source: §1 · pp. 2–3
  • 1.227 BPM MAE, 2.060 BPM RMSE, 0.9934 Pearson correlation, and 92.28% CP3, with 84.6K parameters.Ablations further support complementary contributions from dual-domain learning, interaction-gated fusion, and shared regression.Source: §1 · p. 3

2 Methodology

TF-IG maps preprocessed PPG segments to heart-rate estimates using complementary temporal and frequency branches, interaction-gated fusion, and a shared regression head. The design combines pulse morphology, cardiac periodicity, and learned weighting of the resulting predictions.

2.1 Problem Definition and Notation

  • The model learns a regression function that maps a preprocessed PPG segment to its corresponding reference heart rate.Source: §2.1 · p. 3

2.3 Preprocessing

  • Both branches process the same resampled, z-score-normalized PPG window and produce fixed-dimensional embeddings for fusion.Source: §2.3 · p. 4, §2.2 · p. 4

2.4 Time-Domain Branch

2.5 Frequency-Domain Branch

2.6 Interaction-Gated Fusion Module

2.7 Shared Regression Head with Learnable Ensemble

  • A parameter-shared regression head predicts HR from the temporal, frequency, and fused embeddings, then combines the predictions using learnable normalized weights.Source: §2.7 · pp. 7–8

3 Experimental Settings

Experiments use a subject-exclusive BIDMC split and complementary error, agreement, and coverage metrics. The section also specifies training and checkpoint-selection procedures and identifies Table 1 as a test-split performance and complexity comparison.

3.1 Dataset and Evaluation Metrics

  • The 53 BIDMC subjects were split into 31 training, 11 validation, and 11 held-out test subjects using a fixed random seed of 36.Validation subjects were used for hyperparameter tuning and early stopping; the split was designed to prevent subject-level leakage and evaluate generalization.Source: §3.1 · p. 8
  • MAE, RMSE, and MSE quantify HR error magnitude, Pearson correlation measures linear agreement, and CPk reports the percentage of estimates within k BPM.The evaluation uses six metrics: MAE, RMSE, MSE, Pearson correlation, CP3, and CP5.Source: §3.1 · p. 8

3.2 Implementation Details

  • Models were trained for 150 epochs with Adam on 30-second windows shifted by 2 seconds, and the checkpoint with the lowest validation RMSE was selected.Training used batch size 128, initial learning rate 0.007, weight decay 10^-4, and hidden channel size 64; the learning rate was halved after eight consecutive epochs without validation-loss improvement. The optimization objective was MSE.Source: Training Setup and Hyperparameters · pp. 8–9
  • Table 1 compares performance and complexity on the BIDMC test split under identical experimental protocols.Source: Table 1 · p. 9

4 Results and Discussion

On the subject-level BIDMC evaluation, TF-IG combines strong HR estimation performance with a compact parameter count. Ablations and sensitivity analyses examine the contributions of its components, window duration, and learned representations.

4.1 Main Performance Comparison

  • TF-IG achieved MAE 1.2270 BPM, RMSE 2.0601 BPM, r=0.9934, and CP3=92.28%, exceeding learning-based baselines across these metrics and FCN_Residual by 4.83 percentage points in CP3.Against Welch PSD, TF-IG had slightly higher MAE but lower RMSE and MSE.Source: §4.1 · p. 9

4.2 Model Parameter Analysis

  • With 84,591 trainable parameters, TF-IG remains below 0.1 million despite having more parameters than the three learning-based baselines.The paper describes this alongside superior estimation performance as a favorable accuracy-complexity trade-off.Source: §4.2 · p. 9

4.3 Ablation Study

  • Time-only achieved MAE 2.1677 BPM and RMSE 3.3984 BPM, while frequency-only achieved 2.3470 BPM and 4.5638 BPM; fusion without the interaction gate reached MAE 1.5878 BPM and r=0.9925, while full fusion reached MAE 1.2270 BPM, RMSE 2.0601 BPM, and CP3 92.28%.Replacing the shared head with three separate heads raised MAE from 1.2270 to 1.5020 BPM and lowered CP3 from 92.28% to 84.75%; the full configuration performed best across reported metrics.Source: §4.3 · p. 10

4.4 Window Size Sensitivity Analysis

  • Increasing raw PPG window duration from 16 to 30 seconds lowered MAE from 1.9331 to 1.2270 BPM and RMSE from 3.2854 to 2.0601 BPM.CP3 and CP5 rose by 9.72 and 6.40 percentage points, respectively, and Pearson correlation increased from 0.9856 to 0.9934; the 16-second setting remains an alternative with reduced accuracy.Source: Table 3 · p. 10, §4.4 · p. 11

4.5 Feature Space Representation Analysis

  • In the held-out BIDMC test-set visualization, temporal features formed separated groups across HR ranges, frequency features were more compact by HR, and fused features showed a more balanced organization.The temporal representation may also capture waveform morphology, signal quality, and subject-specific characteristics; neighboring HR ranges still overlapped in the frequency representation.Source: §4.5 · pp. 11–12, Figure 2 · p. 11

5 Conclusion

TF-IG jointly models temporal morphology and spectral periodicity for PPG-based HR estimation. On a subject-exclusive BIDMC split, it outperformed evaluated baselines across most reported metrics while retaining a compact parameter footprint.

  • TF-IG combines temporal morphology and spectral periodicity through interaction-gated fusion and shared regression, with ablations supporting the complementary roles of its components.The subject-exclusive BIDMC evaluation found strong performance across most error, correlation, and strict-accuracy metrics alongside a compact parameter footprint.Source: §5 · p. 12

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