Joint reconstruction of PET-MRI by parallel level sets

Combined positron emission tomography (PET) and magnetic resonance imaging (MRI) scanners acquire simultaneously functional PET and anatomical or functional MRI data. As the data of both modalities are likely to show similar structures we aim to exploit this by joint reconstruction of PET and MRI. In a Bayesian formulation, this can be achieved by adding prior information encoding that the images of the two modalities are not independent. Structural similarity can be modeled by the alignment of the image gradients or equivalently their level sets being parallel. Therefore we can combine the objective functions of both modalities and penalize image pairs which do not have parallel level sets. Our results show that combining the reconstruction from heavily under-sampled MRI and noisy PET data can lead to less under-sampling artifacts in MRI images and better defined PET images.