Joint Non-Linear MRI Inversion with Diffusion Priors

Magnetic resonance imaging (MRI) is a potent diagnostic tool, but suffers from long examination times. To accelerate the process, modern MRI machines typically utilize multiple coils that acquire sub-sampled data in parallel. Data-driven reconstruction approaches, in particular diffusion models, recently achieved remarkable success in reconstructing these data, but typically rely on estimating the coil sensitivities in an off-line step. This suffers from potential movement and misalignment artifacts and limits the application to Cartesian sampling trajectories. To obviate the need for off-line sensitivity estimation, we propose to jointly estimate the sensitivity maps with the image. In particular, we utilize a diffusion model -- trained on magnitude images only -- to generate high-fidelity images while imposing spatial smoothness of the sensitivity maps in the reverse diffusion. The proposed approach demonstrates consistent qualitative and quantitative performance across different sub-sampling patterns. In addition, experiments indicate a good fit of the estimated coil sensitivities.