# Dynamic imaging using Motion-Compensated SmooThness Regularization on Manifolds (MoCo-SToRM)

arXiv: https://arxiv.org/abs/2112.03380 · HTML: https://mlsanity.com/paper/2112.03380/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 50 references that are in the map.
- First posted on arXiv 6 Dec 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [Dynamic imaging using a deep generative SToRM (Gen-SToRM) model](https://mlsanity.com/paper/2102.00034/) (2021)
- [Iterative Motion Compensation reconstruction ultra-short TE(iMoCo UTE) for high resolution free breathing pulmonary MRI](https://mlsanity.com/paper/2001.11993/) (2020)
- [Deep Generative SToRM model for dynamic imaging](https://mlsanity.com/paper/2101.12366/) (2021)
- [Non-rigid 3D motion estimation at high temporal resolution from prospectively undersampled k-space data using low-rank MR-MOTUS](https://mlsanity.com/paper/2007.00488/) (2020)

## Built on by (most cited first, 7 of 7)

- [Deep Learning for Retrospective Motion Correction in MRI: A Comprehensive Review](https://mlsanity.com/paper/2305.06739/) (2023)
- [ICoNIK: Generating Respiratory-Resolved Abdominal MR Reconstructions Using Neural Implicit Representations in k-Space](https://mlsanity.com/paper/2308.08830/) (2023)
- [Motion-compensated MR CINE reconstruction with reconstruction-driven motion estimation](https://mlsanity.com/paper/2302.02504/) (2023)
- [Multi-dynamic deep image prior for cardiac MRI](https://mlsanity.com/paper/2412.04639/) (2024)
- [An unsupervised method for MRI recovery: Deep image prior with structured sparsity](https://mlsanity.com/paper/2501.01482/) (2025)
- [MoRe-3DGSMR: Motion-resolved reconstruction framework for free-breathing pulmonary MRI based on 3D Gaussian representation](https://mlsanity.com/paper/2505.04959/) (2025)
- [Motion-compensated cardiac MRI using low-rank diffeomorphic flow (DMoCo)](https://mlsanity.com/paper/2505.03149/) (2025)

## Abstract (arXiv)

We introduce an unsupervised motion-compensated reconstruction scheme for high-resolution free-breathing pulmonary MRI. We model the image frames in the time series as the deformed version of the 3D template image volume. We assume the deformation maps to be points on a smooth manifold in high-dimensional space. Specifically, we model the deformation map at each time instant as the output of a CNN-based generator that has the same weight for all time-frames, driven by a low-dimensional latent vector. The time series of latent vectors account for the dynamics in the dataset, including respiratory motion and bulk motion. The template image volume, the parameters of the generator, and the latent vectors are learned directly from the k-t space data in an unsupervised fashion. Our experimental results show improved reconstructions compared to state-of-the-art methods, especially in the context of bulk motion during the scans.