In this paper, we formulate the joint/simultaneous X-ray CT and MRI image reconstruction. In particular, a novel algorithm is proposed for MRI image reconstruction from highly under-sampled MRI data and CT images. It consists of two steps. First, a training dataset is generated from a series of well-registered MRI and CT images on the same patients. Then, an initial MRI image of a patient can be reconstructed via edge-oriented dual-dictionary guided enrichment (EDGE) based on the training dataset and a CT image of the patient. Second, an MRI image is reconstructed using the dictionary learning (DL) algorithm from highly under-sampled k-space data and the initial MRI image. Our algorithm can establish a one-to-one correspondence between the two imaging modalities, and obtain a good initial MRI estimation. Both noise-free and noisy simulation studies were performed to evaluate and validate the proposed algorithm. The results with different under-sampling factors show that the proposed algorithm performed significantly better than those reconstructed using the DL algorithm from MRI data alone.
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