Low-Rank Velocity Fields as a Structural Prior for Unsupervised 4D Medical Image Interpolation

Endpoint-only unsupervised 4D medical image interpolation synthesizes intermediate volumes from sparsely sampled sequences with only the start and end volumes available for training; however, this weakly constrained setting often yields intermediates with unstable boundaries and non-physiological motion, limiting interpretability and downstream analysis. We propose low-rank velocity fields as a structural prior, constraining motion to a structured Tucker low-rank velocity field space that decomposes motion into globally shared spatial bases and a compact sample-specific core, thereby encouraging spatially correlated, anatomy-consistent deformation while suppressing voxel-wise high-frequency artifacts. To capture global coordination and local non-rigid details, we model motion in a coarse-to-fine multi-scale scheme and compose scale-wise deformations at inference to synthesize volumes at arbitrary times. We further provide a theoretical analysis showing that, under Tucker parameterization, low-rank parameters control the smoothness energy of the velocity field, explaining why low-rank modeling promotes smoother motion. Experiments on ACDC and 4D-Lung demonstrate state-of-the-art performance, remaining competitive with methods trained with intermediate-frame supervision, and producing intermediates with improved structural coherence and more stable anatomical contours.