Single-Modality Supervised Joint PET-MR Image Reconstruction

We present a new approach for deep learned joint PET-MR image reconstruction. The proposed network is inspired by conventional synergistic methods using a joint regulariser. The maximum a posteriori expectation-maximization algorithm for PET and the Landweber algorithm for MR are unrolled and interconnected through a deep learned joint regularisation step. The parameters of the joint U-Net regulariser and the respective regularisation strengths are learned and shared across all the iterations. Along with introducing this framework, we propose an investigation of the impact of the loss function selection on network performance. We explored how the network performs when trained with a single or a multi-modality loss. Finally, we explored under which settings a joint reconstruction was beneficial for MR reconstruction by using various undersampling factors. The results obtained on 2D simulated data show that the joint networks outperform conventional non-deep learned reconstruction methods, both synergistic and independent. For PET, the network trained with only a PET loss achieves a better global reconstruction accuracy than the version trained with a weighted sum of PET and MR loss terms. More importantly, the former further improves the reconstruction of PET-specific features where deep learned MR-guided methods show their limit. Therefore, using a single-modality loss to supervise the training while still reconstructing the two modalities in parallel leads to better reconstructions and improved modality-unique structure recovery. For MR, while the same effect is observed, the gain from joint reconstruction only occurs in the presence of highly undersampled data.