# Compressed Sensing Plus Motion (CS+M): A New Perspective for Improving Undersampled MR Image Reconstruction

arXiv: https://arxiv.org/abs/1810.10828 · HTML: https://mlsanity.com/paper/1810.10828/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2018.

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

- [Learning-based and unrolled motion-compensated reconstruction for cardiac MR CINE imaging](https://mlsanity.com/paper/2209.03671/) (2022)
- [Motion-compensated MR CINE reconstruction with reconstruction-driven motion estimation](https://mlsanity.com/paper/2302.02504/) (2023)
- [Encoding Enhanced Complex CNN for Accurate and Highly Accelerated MRI](https://mlsanity.com/paper/2306.11977/) (2023)
- [Reconstruction of Cardiac Cine MRI Using Motion-Guided Deformable Alignment and Multi-Resolution Fusion](https://mlsanity.com/paper/2303.04968/) (2023)
- [Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow](https://mlsanity.com/paper/2406.01299/) (2024)
- [Non-rigid Motion Correction for MRI Reconstruction via Coarse-To-Fine Diffusion Models](https://mlsanity.com/paper/2505.15057/) (2025)
- [Flow-Guided Implicit Neural Representation for Motion-Aware Dynamic MRI Reconstruction](https://mlsanity.com/paper/2511.16948/) (2025)

## Abstract (arXiv)

We address the problem of reconstructing high quality images from undersampled MRI data. This is a challenging task due to the highly ill-posed nature of the problem. In particular, in dynamic MRI scans, the interaction between the target structure and the physical motion affects the acquired measurements leading to blurring artefacts and loss of fine details. In this work, we propose a framework for dynamic MRI reconstruction framed under a new multi-task optimisation model called Compressed Sensing Plus Motion (CS+M). Firstly, we propose a single optimisation problem that simultaneously computes the MRI reconstruction and the physical motion. Secondly, we show our model can be efficiently solved by breaking it up into two more computationally tractable problems. The potentials and generalisation capabilities of our approach are demonstrated in different clinical applications including cardiac cine, cardiac perfusion and brain perfusion imaging. We show, through numerical and graphical experiments, that the proposed scheme reduces blurring artefacts and preserves the target shape and fine details. We also report the highest quality reconstruction under highly undersampling rates in comparison to several state of the art techniques.