Spatial and Modal Optimal Transport for Fast Cross-Modal MRI Reconstruction

Multi-modal Magnetic Resonance Imaging (MRI) plays an important role in clinical medicine. However, the acquisitions of some modalities, such as the T2-weighted modality, need a long time and they are always accompanied by motion artifacts. On the other hand, the T1-weighted image (T1WI) shares the same underlying information with T2-weighted image (T2WI), which needs a shorter scanning time. Therefore, in this paper we accelerate the acquisition of the T2WI by introducing the auxiliary modality (T1WI). Concretely, we first reconstruct high-quality T2WIs with under-sampled T2WIs. Here, we realize fast T2WI reconstruction by reducing the sampling rate in the k-space. Second, we establish a cross-modal synthesis task to generate the synthetic T2WIs for guiding better T2WI reconstruction. Here, we obtain the synthetic T2WIs by decomposing the whole cross-modal generation mapping into two OT processes, the spatial alignment mapping on the T1 image manifold and the cross-modal synthesis mapping from aligned T1WIs to T2WIs. It overcomes the negative transfer caused by the spatial misalignment. Then, we prove the reconstruction and the synthesis tasks are well complementary. Finally, we compare it with state-of-the-art approaches on an open dataset FastMRI and an in-house dataset to testify the validity of the proposed method.