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

Multi-modal magnetic resonance imaging (MRI) plays a crucial role in comprehensive disease diagnosis in clinical medicine. However, acquiring certain modalities, such as T2-weighted images (T2WIs), is time-consuming and prone to be with motion artifacts. It negatively impacts subsequent multi-modal image analysis. To address this issue, we propose an end-to-end deep learning framework that utilizes T1-weighted images (T1WIs) as auxiliary modalities to expedite T2WIs' acquisitions. While image pre-processing is capable of mitigating misalignment, improper parameter selection leads to adverse pre-processing effects, requiring iterative experimentation and adjustment. To overcome this shortage, we employ Optimal Transport (OT) to synthesize T2WIs by aligning T1WIs and performing cross-modal synthesis, effectively mitigating spatial misalignment effects. Furthermore, we adopt an alternating iteration framework between the reconstruction task and the cross-modal synthesis task to optimize the final results. Then, we prove that the reconstructed T2WIs and the synthetic T2WIs become closer on the T2 image manifold with iterations increasing, and further illustrate that the improved reconstruction result enhances the synthesis process, whereas the enhanced synthesis result improves the reconstruction process. Finally, experimental results from FastMRI and internal datasets confirm the effectiveness of our method, demonstrating significant improvements in image reconstruction quality even at low sampling rates.