# Non-rigid 3D motion estimation at high temporal resolution from prospectively undersampled k-space data using low-rank MR-MOTUS

arXiv: https://arxiv.org/abs/2007.00488 · HTML: https://mlsanity.com/paper/2007.00488/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 3 of 3)

- [Dynamic imaging using Motion-Compensated SmooThness Regularization on Manifolds (MoCo-SToRM)](https://mlsanity.com/paper/2112.03380/) (2021)
- [Spatiotemporal Gaussian representation-based dynamic reconstruction and motion estimation framework for time-resolved volumetric MR imaging (DREME-GSMR)](https://mlsanity.com/paper/2604.06482/) (2026)
- [Dynamic imaging using motion-compensated smoothness regularization on manifolds (MoCo-SToRM)](https://mlsanity.com/paper/2111.10887/) (2021)

## Abstract (arXiv)

With the recent introduction of the MR-LINAC, an MR-scanner combined with a radiotherapy LINAC, MR-based motion estimation has become of increasing interest to (retrospectively) characterize tumor and organs-at-risk motion during radiotherapy. To this extent, we introduce low-rank MR-MOTUS, a framework to retrospectively reconstruct time-resolved non-rigid 3D+t motion-fields from a single low-resolution reference image and prospectively undersampled k-space data acquired during motion. Low-rank MR-MOTUS exploits spatio-temporal correlations in internal body motion with a low-rank motion model, and inverts a signal model that relates motion-fields directly to a reference image and k-space data. The low-rank model reduces the degrees-of-freedom, memory consumption and reconstruction times by assuming a factorization of space-time motion-fields in spatial and temporal components. Low-rank MR-MOTUS was employed to estimate motion in 2D/3D abdominothoracic scans and 3D head scans. Data were acquired using golden-ratio radial readouts. Reconstructed 2D and 3D respiratory motion-fields were respectively validated against time-resolved and respiratory-resolved image reconstructions, and the head motion against static image reconstructions from fully-sampled data acquired right before and right after the motion. Results show that 2D+t respiratory motion can be estimated retrospectively at 40.8 motion-fields-per-second, 3D+t respiratory motion at 7.6 motion-fields-per-second and 3D+t head-neck motion at 9.3 motion-fields-per-second. The validations show good consistency with image reconstructions. The proposed framework can estimate time-resolved non-rigid 3D motion-fields, which allows to characterize drifts and intra and inter-cycle patterns in breathing motion during radiotherapy, and could form the basis for real-time MR-guided radiotherapy.