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

arXiv: https://arxiv.org/abs/2608.24025 · HTML: https://mlsanity.com/paper/2608.24025/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Diffusion Deformable Model for 4D Temporal Medical Image Generation](https://mlsanity.com/paper/2206.13295/) (2022)
- [Deep Generalization of Structured Low-Rank Algorithms (Deep-SLR)](https://mlsanity.com/paper/1912.03433/) (2019)
- [Fourier-Net: Fast Image Registration with Band-limited Deformation](https://mlsanity.com/paper/2211.16342/) (2022)
- [A Spatiotemporal Volumetric Interpolation Network for 4D Dynamic Medical Image](https://mlsanity.com/paper/2002.12680/) (2020)
- [Data-Efficient Unsupervised Interpolation Without Any Intermediate Frame for 4D Medical Images](https://mlsanity.com/paper/2404.01464/) (2024)
- [Ultrasound Image-to-Video Synthesis via Latent Dynamic Diffusion Models](https://mlsanity.com/paper/2503.14966/) (2025)
- [Self-supervised debiasing using low rank regularization](https://mlsanity.com/paper/2210.05248/) (2022)
- [CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences](https://mlsanity.com/paper/2406.18582/) (2024)
- [FB-Diff: Fourier Basis-guided Diffusion for Temporal Interpolation of 4D Medical Imaging](https://mlsanity.com/paper/2507.04547/) (2025)
- [Real-time non-rigid 3D respiratory motion estimation for MR-guided radiotherapy using MR-MOTUS](https://mlsanity.com/paper/2104.07957/) (2021)
- [Coarse-Super-Resolution-Fine Network (CoSF-Net): A Unified End-to-End Neural Network for 4D-MRI with Simultaneous Motion Estimation and Super-Resolution](https://mlsanity.com/paper/2211.11144/) (2022)
- [AIF-SFDA: Autonomous Information Filter-driven Source-Free Domain Adaptation for Medical Image Segmentation](https://mlsanity.com/paper/2501.03074/) (2025)
- [Online 4D Ultrasound-Guided Robotic Tracking Enables 3D Ultrasound Localisation Microscopy with Large Tissue Displacements](https://mlsanity.com/paper/2409.11391/) (2024)

## Abstract (arXiv)

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.