Multi-shot diffusion-weighted MRI reconstruction with magnitude-based spatial-angular locally low-rank regularization (SPA-LLR)

Purpose: To resolve the motion-induced phase variations in multi-shot multi-direction diffusion-weighted imaging (DWI) by applying regularization to magnitude images.

Theory and methods: A nonlinear model was developed to estimate phase and magnitude images separately. A locally low-rank regularization (LLR) term was applied to the magnitude images from all diffusion-encoding directions to exploit the spatial and angular correlation. In vivo experiments with different resolutions and b-values were performed to validate the proposed method.

Results: The proposed method significantly reduces the noise level compared to the conventional reconstruction method and achieves submillimeter (0.8mm and 0.9mm isotropic resolutions) DWI with a b-value of 1,000 $s/{\text{mm}}^2$ and 1-mm isotropic DWI with a b-value of 2,000 $s/{\text{mm}}^2$ without modification of the sequence.

Conclusions: A joint reconstruction method with spatial-angular LLR regularization on magnitude images substantially improves multi-direction DWI reconstruction, simultaneously removes motion-induced phase artifacts, and denoises images.