CycleSpectra: Cyclic Motion Spectra for Phase-Queryable 4D Cardiac Reconstruction

Reconstructing patient-specific cyclic cardiac motion at arbitrary phases is central to dynamic cardiac assessment, underpinning measurements such as ejection fraction, stroke volume, and regional myocardial deformation. Existing methods---pair-wise registration, time-conditioned decoders, and coordinate-based implicit fields---share a common implicit assumption: the cardiac cycle is treated as a sequence of discrete phases, with temporal structure stitched together through learned mappings supervised at the observed frames. Yet the cycle is, by physical fact, a closed periodic process. We propose \textbf{CycleSpectra}, a spectral motion representation that takes the cyclic structure as a starting point of the representation rather than as a property to be learned. Given a pair of sparsely sampled phase observations, the model learns the spectral structure of the underlying cyclic cardiac motion in a low-dimensional latent space, and recovers the displacement at any phase through a fixed analytic synthesis layer---time never enters the network as a learnable signal, only as a coordinate the readout takes by construction. To support evaluation, we collect a thin-slice phase-resolved 4D cardiac CT cohort and benchmark under both canonical and non-canonical input protocols, reporting whole-cycle motion-fidelity metrics alongside standard image and anatomical metrics. Under arbitrary two-frame input, CycleSpectra achieves the lowest ejection-fraction error and highest ventricular volume--time curve correlation among recent baselines, while remaining competitive on image fidelity. Beyond two-frame inference, the proposed framework supports test-time multi-frame latent fusion for higher accuracy, validated on both the in-house cohort and a cross-modality 4D cardiac MR cohort. Code will be available.