# Motion-compensated cardiac MRI using low-rank diffeomorphic flow (DMoCo)

arXiv: https://arxiv.org/abs/2505.03149 · HTML: https://mlsanity.com/paper/2505.03149/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 41 references that are in the map.
- First posted on arXiv 6 May 2025.

## Builds on (most cited first, 13 of 13)

- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [Neural Implicit k-Space for Binning-free Non-Cartesian Cardiac MR Imaging](https://mlsanity.com/paper/2212.08479/) (2022)
- [Learning Energy-Based Models in High-Dimensional Spaces with Multi-scale Denoising Score Matching](https://mlsanity.com/paper/1910.07762/) (2019)
- [Dynamic imaging using a deep generative SToRM (Gen-SToRM) model](https://mlsanity.com/paper/2102.00034/) (2021)
- [ICoNIK: Generating Respiratory-Resolved Abdominal MR Reconstructions Using Neural Implicit Representations in k-Space](https://mlsanity.com/paper/2308.08830/) (2023)
- [Multi-Scale Energy (MuSE) plug and play framework for inverse problems](https://mlsanity.com/paper/2305.04775/) (2023)
- [Iterative Motion Compensation reconstruction ultra-short TE(iMoCo UTE) for high resolution free breathing pulmonary MRI](https://mlsanity.com/paper/2001.11993/) (2020)
- [Dynamic imaging using Motion-Compensated SmooThness Regularization on Manifolds (MoCo-SToRM)](https://mlsanity.com/paper/2112.03380/) (2021)
- [Variational manifold learning from incomplete data: application to multislice dynamic MRI](https://mlsanity.com/paper/2101.08196/) (2021)
- [Motion-robust free-running volumetric cardiovascular MRI](https://mlsanity.com/paper/2308.02088/) (2023)
- [Multi-dynamic deep image prior for cardiac MRI](https://mlsanity.com/paper/2412.04639/) (2024)
- [Accelerated Real-time Cine and Flow under In-magnet Staged Exercise](https://mlsanity.com/paper/2402.17877/) (2024)

## Abstract (arXiv)

We introduce an unsupervised motion-compensated image reconstruction algorithm for free-breathing and ungated 3D cardiac magnetic resonance imaging (MRI). We express the image volume corresponding to each specific motion phase as the deformation of a single static image template. The main contribution of the work is the low-rank model for the compact joint representation of the family of diffeomorphisms, parameterized by the motion phases. The diffeomorphism at a specific motion phase is obtained by integrating a parametric velocity field along a path connecting the reference template phase to the motion phase. The velocity field at different phases is represented using a low-rank model. The static template and the low-rank motion model parameters are learned directly from the k-space data in an unsupervised fashion. The more constrained motion model is observed to offer improved recovery compared to current motion-resolved and motion-compensated algorithms for free-breathing 3D cine MRI.