A diffusion-weighted magnetic resonance imaging (MRI) method acquires MRI scan data from a multi-direction, multi-shot, diffusion-weighted MRI scan, and jointly reconstructs from the MRI scan data 1) magnitude images for multiple diffusion-encoding directions and 2) phase images for multiple shots and multiple diffusion-encoding directions using an iterative reconstruction method. Each iteration of the iterative reconstruction method comprises a gradient calculation, a phase update to update the phase images, and a magnitude update to update the magnitude images. Each iteration minimizes a cost function comprising a locally low-rank (LLR) regularization constraint on the magnitude images from the multiple diffusion-encoding directions.
Diffusion-weighted MRI with magnitude-based locally low-rank regularization