  Magnetic resonance imaging (MRI) is known to have reduced signal-to-noise
ratios (SNR) at lower field strengths, leading to signal degradation when
producing a low-field MRI image from a high-field one. Therefore,
reconstructing a high-field-like image from a low-field MRI is a complex
problem due to the ill-posed nature of the task. Additionally, obtaining paired
low-field and high-field MR images is often not practical. We theoretically
uncovered that the combination of these challenges renders conventional deep
learning methods that directly learn the mapping from a low-field MR image to a
high-field MR image unsuitable. To overcome these challenges, we introduce a
novel meta-learning approach that employs a teacher-student mechanism. Firstly,
an optimal-transport-driven teacher learns the degradation process from
high-field to low-field MR images and generates pseudo-paired high-field and
low-field MRI images. Then, a score-based student solves the inverse problem of
reconstructing a high-field-like MR image from a low-field MRI within the
framework of iterative regularization, by learning the joint distribution of
pseudo-paired images to act as a regularizer. Experimental results on real
low-field MRI data demonstrate that our proposed method outperforms
state-of-the-art unpaired learning methods.
