Moner: Motion Correction in Undersampled Radial MRI with Unsupervised Neural Representation

TL;DR

Moner introduces an unsupervised neural representation approach for motion correction in radial MRI that does not require training data, effectively reconstructing artifact-free images and estimating motion from undersampled, corrupted data.

Contribution

It proposes a novel unsupervised method leveraging implicit neural representations and a coarse-to-fine hash encoding for improved motion correction in radial MRI without training data.

Findings

Achieves comparable performance to state-of-the-art methods on in-domain data.

Shows significant improvements on out-of-domain data.

Does not require large-scale training datasets.

Abstract

Motion correction (MoCo) in radial MRI is a particularly challenging problem due to the unpredictability of subject movement. Current state-of-the-art (SOTA) MoCo algorithms often rely on extensive high-quality MR images to pre-train neural networks, which constrains the solution space and leads to outstanding image reconstruction results. However, the need for large-scale datasets significantly increases costs and limits model generalization. In this work, we propose Moner, an unsupervised MoCo method that jointly reconstructs artifact-free MR images and estimates accurate motion from undersampled, rigid motion-corrupted k-space data, without requiring any training data. Our core idea is to leverage the continuous prior of implicit neural representation (INR) to constrain this ill-posed inverse problem, facilitating optimal solutions. Specifically, we integrate a quasi-static motion model into the INR, granting its ability to correct subject's motion. To stabilize model optimization, we reformulate radial MRI reconstruction as a back-projection problem using the Fourier-slice theorem. Additionally, we propose a novel coarse-to-fine hash encoding strategy, significantly enhancing MoCo accuracy. Experiments on multiple MRI datasets show our Moner achieves performance comparable to SOTA MoCo techniques on in-domain data, while demonstrating significant improvements on out-of-domain data. The code is available at: https://github.com/iwuqing/Moner