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This paper introduces low-rank velocity fields as a structural prior for unsupervised 4D medical image interpolation, addressing the challenge of synthesizing intermediate volumes from sparsely sampled sequences. By constraining motion to a Tucker low-rank velocity field space, the method promotes anatomy-consistent deformation and reduces high-frequency artifacts, resulting in smoother and more interpretable intermediate images. Experimental results on the ACDC and 4D-Lung datasets show that this approach achieves state-of-the-art performance, even outperforming methods that rely on intermediate-frame supervision.
Low-rank velocity fields can transform unsupervised 4D medical image interpolation, yielding anatomically coherent results that rival supervised methods.
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.
