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Magnetic Resonance Imaging (MRI) stands as a powerful modality in clinicaldiagnosis. However, it is known that MRI faces challenges such as longacquisition time and vulnerability to motion-induced artifacts. Despite thesuccess of many existing motion correction algorithms, there has been limitedresearch focused on correcting motion artifacts on the estimated coilsensitivity maps for fast MRI reconstruction. Existing methods might sufferfrom severe performance degradation due to error propagation resulting from theinaccurate coil sensitivity maps estimation. In this work, we propose tojointly estimate the motion parameters and coil sensitivity maps forunder-sampled MRI reconstruction, referred to as JSMoCo. However, jointestimation of motion parameters and coil sensitivities results in a highlyill-posed inverse problem due to an increased number of unknowns. To addressthis, we introduce score-based diffusion models as powerful priors and leveragethe MRI physical principles to efficiently constrain the solution space forthis optimization problem. Specifically, we parameterize the rigid motion asthree trainable variables and model coil sensitivity maps as polynomialfunctions. Leveraging the physical knowledge, we then employ Gibbs sampler forjoint estimation, ensuring system consistency between sensitivity maps anddesired images, avoiding error propagation from pre-estimated sensitivity mapsto the reconstructed images. We conduct comprehensive experiments to evaluatethe performance of JSMoCo on the fastMRI dataset. The results show that ourmethod is capable of reconstructing high-quality MRI images fromsparsely-sampled k-space data, even affected by motion. It achieves this byaccurately estimating both motion parameters and coil sensitivities,effectively mitigating motion-related challenges during MRI reconstruction.

JSMoCo: Joint Coil Sensitivity and Motion Correction in Parallel MRI with a Self-Calibrating Score-Based Diffusion Model