Unsupervised Accelerated MRI Reconstruction via Ground-Truth-Free Flow Matching

Abstract

Accelerated magnetic resonance imaging involves reconstructing fully sampled images from undersampled k-space measurements. Current state-of-the-art approaches have mainly focused on either end-to-end supervised training inspired by compressed sensing formulations, or posterior sampling methods built on modern generative models. However, their efficacy heavily relies on large datasets of fully sampled images, which may not always be available in practice. To address this issue, we propose an unsupervised MRI reconstruction method based on ground-truth-free flow matching (GTF$^2$M). Particularly, the GTF$^2$M learns a prior denoising process of fully sampled ground-truth images using only undersampled data. Based on that, an efficient cyclic reconstruction algorithm is further proposed to perform forward and backward integration in the dual space of image-space signal and k-space measurement. We compared our method with state-of-the-art learning-based baselines on the fastMRI database of both single-coil knee and multi-coil brain MRIs. The results show that our proposed unsupervised method can significantly outperform existing unsupervised approaches, and achieve performance comparable to most supervised end-to-end and prior learning baselines trained on fully sampled MRI, while offering greater efficiency than the compared generative model-based approaches.