Joint coil sensitivity and motion correction in parallel MRI with a self-calibrating score-based diffusion model

Magnetic Resonance Imaging (MRI) stands as a powerful modality in clinical diagnosis. However, it faces challenges such as long acquisition time and vulnerability to motion-induced artifacts. While many existing motion correction algorithms have shown success, most fail to account for the impact of motion artifacts on coil sensitivity map (CSM) estimation during fast MRI reconstruction. This oversight can lead to significant performance degradation, as errors in the estimated CSMs can propagate and compromise motion correction. In this work, we propose JSMoCo, a novel method for jointly estimating motion parameters and time-varying coil sensitivity maps for under-sampled MRI reconstruction. The joint estimation presents a highly ill-posed inverse problem due to the increased number of unknowns. To address this challenge, we leverage score-based diffusion models as powerful priors and apply MRI physical principles to effectively constrain the solution space. Specifically, we parameterize rigid motion with trainable variables and model CSMs as polynomial functions. A Gibbs sampler is employed to ensure system consistency between the sensitivity maps and the reconstructed images, effectively preventing error propagation from pre-estimated sensitivity maps to the final reconstructed images. We evaluate JSMoCo through 2D and 3D motion correction experiments on simulated motion-corrupted fastMRI dataset and in-vivo real MRI brain scans. The results demonstrate that JSMoCo successfully reconstructs high-quality MRI images from under-sampled k-space data, achieving robust motion correction by accurately estimating time-varying coil sensitivities. The code is available at https://github.com/MeijiTian/JSMoCo.