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

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

cs.LGOct 20, 2026

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

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

Organizations: International University, Vietnam National University HCMC, Ho Chi Minh City, Vietnam · University of New Brunswick, Fredericton, Canada · Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam · Austrian Institute of Technology, Vienna, Austria

Abstract

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.

Figures & tables

Figure 1: Overview structure of proposed framework

Model	Params	FLOPs/sample	MAE (BPM) $\downarrow$	RMSE (BPM) $\downarrow$	MSE $\downarrow$	Pearson $r$ $\uparrow$	$CP_{5}$ (%) $\uparrow$	$CP_{3}$ (%) $\uparrow$
TF-IG (Ours)	84,591	13.46 M	1.2270	2.0601	4.2440	0.9934	95.98	92.28
Welch PSD [ 11 ]	0	N/A	1.0823	3.2015	10.2494	0.9810	93.24	90.79
FCN_Residual [ 16 ]	53,713	99.52 M	1.5584	2.1180	4.4860	0.9918	97.79	87.45
FCN [ 16 ]	8,945	8.47 M	2.9695	3.7681	14.1986	0.9824	85.72	61.10
FCN_DCT [ 16 ]	3,266	0.573 M	5.8389	8.0721	65.1582	0.9122	57.68	36.85

Table 1: Performance and complexity comparison on the BIDMC test split under identical experimental protocols.

Time Branch	Freq Branch	Int-Gated Fusion	Shared Head	MAE $\downarrow$	RMSE $\downarrow$	MSE $\downarrow$	Pearson $r$ $\uparrow$	$CP_{3}$ (%) $\uparrow$	$CP_{5}$ (%) $\uparrow$
✓	$\times$	$\times$	✓	2.1677	3.3984	11.5492	0.9862	78.52	87.77
$\times$	✓	$\times$	✓	2.347	4.5638	20.8283	0.9713	83.31	89.02
✓	✓	$\times$	✓	1.5878	2.464	6.0713	0.9925	87.17	92.24
✓	✓	✓	$\times$	1.502	2.4475	5.9904	0.9926	84.75	93.85
✓	✓	✓	✓	1.227	2.0601	4.244	0.9934	92.28	95.98

Table 2: Ablation study evaluating the contribution of individual architectural components.

Raw Window	MAE (BPM) $\downarrow$	RMSE (BPM) $\downarrow$	MSE $\downarrow$	Pearson $r$ $\uparrow$	$CP_{3}$ (%) $\uparrow$	$CP_{5}$ (%) $\uparrow$
$16$ seconds	1.9331	3.2854	10.7938	0.9856	82.56	89.58
$30$ seconds	1.2270	2.0601	4.2440	0.9934	92.28	95.98

Table 3: Performance of TF-IG with different raw PPG window durations before resampling.

Figure 2: t-SNE visualization of the representations learned by TF-IG on the BIDMC test split: (a) temporal features

\mathbf{z}_{t}

, (b) frequency features

\mathbf{z}_{f}

, and (c) fused features

\mathbf{z}_{\mathrm{fuse}}

. Colors indicate reference-HR ranges.

Heart Rate Estimation

Heart rate estimation recovers beats per minute from wearable, contact, or remote physiological signals.

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Jun 29, 2026

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

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.

Nouhaila Fraihi, Ouassim Karrakchou, Mounir Ghogho

1TICLab, International University of Rabat, Morocco · College of Computing, Mohammed VI Polytechnic University, Morocco · Faculty of Engineering, University of Leeds, UK

Heart Rate Estimation Physics-Informed ML Photoplethysmography Wearable Health Monitoring

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May 19, 2026

Cross-View Attention Fusion Net: A Prior-Guided Dual-View Representation Learning for Cardiac Output Estimation from Short-Term PPG Signals

Accurate cardiac output (CO) estimation from photoplethysmography (PPG) is promising for unobtrusive hemodynamic monitoring, but remains difficult since CO is jointly determined by cardiac function and vascular tone. Conventional feature-based models use physiologically meaningful PPG descriptors, yet depend on accurate pulse detection and may miss latent temporal relationships. In contrast, fully end-to-end deep learning models learn directly from raw PPG but often underuse established PPG-derived prior information. Here, we introduce the Cross-View Attention Fusion Network (CVAF-Net), a prior-guided dual-view deep learning model for CO estimation from short, fixed-length PPG segments. CVAF-Net processes raw PPG as a temporal view and a feature sequence map (FSM) as a structured prior-guided view, and fuses the two representations through cross-view attention. The model was independently evaluated using 5-, 15-, and 30-s segments from three datasets: simulated pulse waves (3323 subjects), vasoconstriction provocation (79 subjects), and resting/cycling activities (10 subjects), and was compared with multiple machine learning and deep learning benchmarks. CVAF-Net outperformed most benchmark methods and achieved performance comparable to a state-of-the-art Transformer-based model, with a mean absolute error (MAE) of 0.19 L/min (MAPE: 3.95%) on simulated data and high accuracy in real-world settings (minimum MAE: 1.20 L/min). Importantly, CVAF-Net reduced FLOPs by twelvefold compared with the leading Transformer-based model. Plausibility analysis showed physiologically consistent CO estimates, with expected correlations with age (

ρ= -0.274

), heart rate (

ρ= 0.894

), and systemic vascular resistance (

ρ= -0.740

). These findings indicate that CVAF-Net provides an accurate, computationally efficient, and generalizable approach for continuous wearable-based CO monitoring.

Yaowen Zhang, Bo Cui, Libera Fresiello +3

Department of Biomedical Signals and Systems, University of Twente, Enschede, 7522NB, The Netherlands · Department of Cardiovascular and Respiratory Physiology, University of Twente, Enschede, 7522NB, The Netherlands · Department of Intensive Care, University Medical Center Utrecht, Utrecht, 3584CX, The Netherlands

Photoplethysmography

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Aug 16, 2026

CardiacMamba: Fair and Robust RGB-RF Fusion for Remote Heart Rate Estimation via State Space Modeling

Remote photoplethysmography (rPPG) enables non-contact heart rate (HR) monitoring from facial videos, but RGB-only methods are vulnerable to illumination changes, motion artifacts, and skin-tone-dependent optical reflectance. We propose CardiacMamba, a fair and robust RGB-RF fusion framework that integrates optical facial cues and radio-frequency cardiac motion cues through state space modeling. CardiacMamba introduces a Temporal Difference Mamba Module (TDMM) to enhance subtle RF temporal variations, a bidirectional SSM-based interaction mechanism to align heterogeneous RGB-RF dynamics, and a Channel-wise Fast Fourier Transform (CFFT) module for channel-domain spectral refinement. On the EquiPleth dataset, CardiacMamba achieves state-of-the-art performance with 0.96 bpm MAE, 3.06 bpm RMSE, and 0.97 Pearson correlation, while reducing the observed light-dark skin-tone MAE gap to 0.26 bpm and maintaining robustness under RGB degradation and RF-missing conditions

Bo Zhao, Zheng Wu, Yiping Xie +1

Great Bay University

Heart Rate Estimation Remote Photoplethysmography Camera-Radar Fusion Multimodal Sensor Fusion State Space Models Algorithmic Fairness

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Abstract

Heart Rate Estimation

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