Motion correction (MoCo) in radial MRI is a challenging problem due to the unpredictability of subject's motion. Current state-of-the-art (SOTA) MoCo algorithms often use extensive high-quality MR images to pre-train neural networks, obtaining excellent reconstructions. 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 solves artifact-free MR images and accurate motion from undersampled, rigid motion-corrupted k-space data, without requiring training data. Our core idea is to leverage the continuous prior of implicit neural representation (INR) to constrain this ill-posed inverse problem, enabling ideal solutions. Specifically, we incorporate a quasi-static motion model into the INR, granting its ability to correct subject's motion. To stabilize model optimization, we reformulate radial MRI 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.

翻译：径向磁共振成像中的运动校正是一个具有挑战性的问题，这主要源于被试者运动的不确定性。当前最先进的运动校正算法通常需要使用大量高质量磁共振图像对神经网络进行预训练，以获得优异的重建效果。然而，大规模数据集的需求显著增加了成本并限制了模型的泛化能力。在本工作中，我们提出了一种名为Moner的无监督运动校正方法，该方法无需训练数据，能够从欠采样的、存在刚性运动伪影的k空间数据中联合求解出无伪影的磁共振图像和精确的运动参数。我们的核心思想是利用隐式神经表示的连续性先验来约束这一病态逆问题，从而获得理想的解。具体而言，我们将一个准静态运动模型融入隐式神经表示中，使其具备校正被试者运动的能力。为了稳定模型优化，我们利用傅里叶切片定理将径向磁共振成像重新表述为一个反投影问题。此外，我们提出了一种新颖的由粗到精的哈希编码策略，显著提升了运动校正的精度。在多个磁共振成像数据集上的实验表明，我们的Moner方法在域内数据上取得了与最先进运动校正技术相当的性能，同时在域外数据上展现出显著的改进。