# Multi-tasking to Correct: Motion-Compensated MRI via Joint Reconstruction and Registration

## TL;DR

This paper presents a novel variational model for MRI motion correction that jointly reconstructs motion-free images and estimates physiological dynamics, outperforming sequential methods in quality and artifact reduction.

## Contribution

It introduces a combined reconstruction-registration variational model with hyperelastic regularization for large deformations in MRI motion correction.

## Key findings

- Higher quality reconstructions with better contrast and detail
- Effective estimation of breathing dynamics
- Outperforms sequential approaches in artifact reduction

## Abstract

This work addresses a central topic in Magnetic Resonance Imaging (MRI) which is the motion-correction problem in a joint reconstruction and registration framework. From a set of multiple MR acquisitions corrupted by motion, we aim at - jointly - reconstructing a single motion-free corrected image and retrieving the physiological dynamics through the deformation maps. To this purpose, we propose a novel variational model. First, we introduce an $L^2$ fidelity term, which intertwines reconstruction and registration along with the weighted total variation. Second, we introduce an additional regulariser which is based on the hyperelasticity principles to allow large and smooth deformations. We demonstrate through numerical results that this combination creates synergies in our complex variational approach resulting in higher quality reconstructions and a good estimate of the breathing dynamics. We also show that our joint model outperforms in terms of contrast, detail and blurring artefacts, a sequential approach.