This paper introduces a motion-corrected, free-breathing dynamic contrast-enhanced (DCE) MRI reconstruction method, termed low-rank plus sparse (L+S) with soft weighting. We designed a soft weighting matrix that smoothly transitions spokes between the target and other motion states to suppress motion blurring. The optimized fast iterative shrinkage-thresholding algorithm (FISTA) was employed to solve the L+S optimization problem, enabling faster convergence and better image quality. A DCE-MRI computer simulation framework, based on a modified Shepp-Logan model, was used as ground truth to quantify the motion suppression errors. Both simulation and clinical datasets demonstrate that the proposed method provides superior motion correction, higher temporal resolution, and over 5 times faster reconstruction speed than existing motion-corrected GRASP frameworks.
