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

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.

Estimating electrocardiography (ECG) from a chest-worn inertial measurement unit (IMU) enables continuous heart rate (HR) monitoring without the discomfort of electrodes. We propose TinyCardioUNet, a lightweight UNet that uses all six IMU axes without prior channel selection, refines its bottleneck with a graph neural network that encodes inter-axis dependencies, and employs tensor decomposition with automatic variational Bayesian rank selection for parameter reduction. On a public dataset, TinyCardioUNet achieves an RMSE of $0.098$ and a Pearson correlation coefficient of $0.677$ with only $36.0$k parameters and remains comparatively robust to additive noise, demonstrating accurate ECG reconstruction with a compact model.

Cardiac function evaluation necessitates continuous, non-invasive monitoring, a capability limited in MRI. Millimeter-wave (mmWave) radar and its Synthetic Aperture Radar (SAR) mode offer a privacy-preserving and portable point-of-care clinical applications. However, reconstructing high-fidelity 3D cardiac geometry from SAR remains an open challenge. Traditional radar methods generate sparse point clouds that lack continuous surface topology. Meanwhile, direct application of optical reconstruction networks performs poorly due to the severe speckle noise and ambiguous boundaries inherent in SAR images. To bridge this gap, we propose SAR2Mesh, a novel framework that reformulates the task as a coarse-to-fine mesh deformation process. By initializing with a topological template, our approach explicitly preserves anatomical connectivity through progressive mesh deformation.We introduce a geometry-aware feature projection module to extract multi-view features via 3D-to-2D sampling, and a physics-informed radar loss to enforce consistency between the predicted geometry and raw radar echoes. Furthermore, we present Cardiac Mesh-SAR, the first large-scale paired SAR-mesh dataset. Extensive experiments demonstrate that SAR2Mesh significantly outperforms existing image-based baselines, achieving accurate and physically consistent cardiac reconstructions.