Multi-shot diffusion-weighted imaging reconstructions are challenged by the inter-shot phase inconsistency that exists between the data from different shots. The MUSSELS algorithm enabled the direct reconstruction of the multi-shot k-space data by posing it as a low-rank based matrix recovery problem. The iterative algorithm has been shown to successfully recover the missing k-space samples in accelerated and non-accelerated acquisitions. However, the reconstruction time increases as the number of shots\acceleration increases. We propose a new formulation based on iterative re-weighted least squares that increase the computational efficiency of the matrix completion by several folds to speed up the recovery of multi-shot data.