Multi-shot diffusion-weighted magnetic resonance imaging acquires multiple k-space segments of diffusion-weighted MRI data, estimates reconstructed multi-shot diffusion weighted images, and combines the estimated images to obtain a final reconstructed MRI image. The estimation of images iteratively calculates updated multi-shot images from the multiple k-space segments and current multi-shot images using a convex model without estimating motion-induced phase, constructs multiple locally low-rank spatial-shot matrices from the updated multi-shot images, and calculates current multi-shot images from spatial-shot matrices.