Kapture: Capturing Cardiac Dynamics with Koopman-Governed Learning for Efficient Radar-Based Electrocardiogram Recovery

Tong Wu; Jing Peng; Ziqi Feng; Yuanyuan Zhang

eess.SPOct 4, 2026

Kapture: Capturing Cardiac Dynamics with Koopman-Governed Learning for Efficient Radar-Based Electrocardiogram Recovery

Authors: Tong Wu, Jing Peng, Ziqi Feng, Yuanyuan Zhang

Organizations: Amazon, Seattle, Washington, United States · Equitable, Waterloo, Canada · School of Psychology & Neuroscience, University of Glasgow, Glasgow, United Kingdom

Abstract

Millimeter-wave (mmWave) radar enables unobtrusive, contactless electrocardiogram (ECG) reconstruction for cardiac monitoring. Time-frequency spectrograms preserve fine cardiac patterns but often require large backbones to separate ECG-relevant features from respiration, motion, multipath, and subject-dependent interference. We propose Kapture, a parameter-efficient Koopman-governed framework that projects radar hidden states into a low-dimensional observable space and identifies a regularized full linear evolution operator from adjacent observable states. The Koopman-predicted observables refine subsequent hidden states for ECG reconstruction. To suppress predictable interference dynamics, a temporal contrastive objective pulls neighboring states together and separates non-neighbors, while reconstruction supervision preserves task relevance. Using approximately 80 minutes of quasi-static radar-ECG recordings containing realistic noise from body movements and other sources, Kapture consistently improves reconstruction across matched backbone widths, with the largest gains under aggressive compression. The compact configuration approaches the full-width reference accuracy with 68.1% fewer parameters and 91.3% fewer profiler-covered floating-point operations (FLOPs), while the full-width configuration delivers the strongest overall reconstruction performance. Our code will be made publicly available after potential publication.

Figures & tables

Figure 1: Overview of the Kapture framework: (a) Lightweight radar-to-ECG feature encoding and waveform recovery; (b) Ridge-identified Koopman feature evolution; (c) Joint objectives for Koopman consistency, information regularization, and ECG reconstruction.

	ECG recovery		Deployment efficiency
Model	nMSE $\downarrow$	PCC $\uparrow$	Parameters $\downarrow$	FLOPs $\downarrow$
	( $\times 10^{-2}$ )	(%)	( $10^{6}$ )	( $10^{9}$ )
RaECG [ 9 ]	$1.55$	$83.14$	2.887	0.691
Con-Diff [ 15 ]	$1.95$	$80.49$	$\mathbf{0.907}$	11.196
mmJEPA [ 8 ]	$2.26$	$75.24$	$\underline{2.141}$	22.985
Baseline ( $D{=}64$ )	$2.32$	$79.34$	2.612	$\mathbf{0.104}$

Table 1: Performance of different methods and matched Koopman ablations across backbone widths.

	Loss			ECG recovery
Configuration	$\mathcal{L}_{\mathrm{KEC}}$	$\mathcal{L}_{\mathrm{NCE}}$	$\mathcal{H}_{\mathrm{vN}}$	nMSE $\downarrow$	PCC $\uparrow$
				( $\times 10^{-2}$ )	(%)
Koopman only	$\checkmark$	–	–	$1.61$	$\underline{81.47}$
$+\mathcal{L}_{\mathrm{NCE}}$	$\checkmark$	$\checkmark$	–	$\underline{1.56}$	$79.43$
$+$ entropy	$\checkmark$	–	$\checkmark$	$1.60$	$77.96$
Full objective	$\checkmark$	$\checkmark$	$\checkmark$	$\mathbf{1.54}$	$\mathbf{85.10}$

Table 2: Ablation of the loss terms for Kapture (

D=128

Figure 2: Recovered ECG with ground truth in gray: (a) - (d) Results from different models.

Figure 3: Accuracy–efficiency comparison; marker shape identifies the model variant and bubble area indicates parameter count.

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BeatFlow-ECG: Rectified Flow for ECG Reconstruction from Indirect Wearable Signals

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Continuous cardiac monitoring outside clinical settings requires signals that are both informative and practical to collect during daily life. Electrocardiography (ECG) provides rich information about cardiac rhythm and waveform morphology, while wearable photoplethysmography (PPG) is easier to acquire continuously but is only an indirect cardiovascular measurement and is highly sensitive to motion. We present BeatFlow-ECG, a conditional rectified-flow model for reconstructing single-channel ECG from synchronized PPG and inertial measurements. BeatFlow-ECG models reconstruction as conditional transport from noise to ECG using a convolutional encoder-decoder with a transformer bottleneck and explicit flow-time conditioning. Motion information is incorporated through IMU-derived conditioning features, motion-dependent loss weighting, and an easy-to-hard training curriculum. We evaluate the model under leave-one-subject-out protocols on PPG-DaLiA and WESAD. BeatFlow-ECG achieves the best results among the evaluated deterministic, adversarial, and diffusion-based baselines across all reported waveform and beat-timing metrics, with Pearson correlations of 0.983 and 0.986 and R-peak F1 scores of 0.946 and 0.955, respectively. Compared with Conditional DDPM-1D, L1 error decreases from 0.085 to 0.062 on PPG-DaLiA and from 0.074 to 0.055 on WESAD. Additional analyses on PPG-DaLiA show higher correlation in fixed R-peak-relative waveform regions and lower reconstruction error across low-, medium-, and high-motion subsets.

Abstract

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