Title: Unsupervised Parallel MRI Reconstruction via Projected Conditional Flow Matching
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
Keywords: unsupervised learning, MRI reconstruction, flow matching, generative models

Abstract: Reconstructing high-quality images from substantially undersampled k-space data for accelerated MRI presents a challenging ill-posed inverse problem. Supervised deep learning has transformed the field by using large amounts of fully sampled ground-truth MR images, either to directly reconstruct undersampled data into fully sampled images with neural networks, or to learn the prior distribution of fully sampled images through generative models. However, in practical scenarios, acquiring ground-truth fully sampled MRI images is not viable due to the inherently slow nature of its data acquisition process. Despite advances in self-supervised/unsupervised MRI reconstruction, the performance remains inadequate at high acceleration rates. To address these gaps, we introduce the Projected Conditional Flow Matching (PCFM) and its unsupervised transformation, which is designed to learn the prior distribution of fully sampled parallel MRI by solely utilizing the undersampled k-space measurements. To reconstruct the image, we establish a novel relationship between the marginal vector field in the measurement space, which generates the associated probability flow in terms of the continuity equation, and the optimal solution to PCFM. This connection results in a cyclic dual-space sampling algorithm for unsupervised reconstruction. Our method was evaluated against contemporary state-of-the-art supervised, self-supervised, and unsupervised baseline techniques on parallel MRI using publicly available datasets fastMRI and CMRxRecon. Experimental results show that our technique significantly surpasses existing self-supervised and unsupervised baselines, while also yielding better performance than most supervised methods. Our code will be available at \url{https://github.com/anonymous}.