  Purpose: To introduce a novel method for the recovery of multi-shot diffusion
weighted (MS-DW) images from echo-planar imaging (EPI) acquisitions.
  Methods: Current EPI-based MS-DW reconstruction methods rely on the explicit
estimation of the motion- induced phase maps to recover the unaliased images.
In the new formulation, the k-space data of the unaliased DWI is recovered
using a structured low-rank matrix completion scheme, which does not require
explicit estimation of the phase maps. The structured matrix is obtained as the
lifting of the multi-shot data. The smooth phase-modulations between shots
manifest as null-space vectors of this matrix, which implies that the
structured matrix is low-rank. The missing entries of the structured matrix are
filled in using a nuclear-norm minimization algorithm subject to the
data-consistency. The formulation enables the natural introduction of
smoothness regularization, thus enabling implicit motion-compensated recovery
of fully-sampled as well as under-sampled MS-DW data.
  Results: Our experiments on in-vivo data show effective removal of the
ghosting artifacts arising from intershot motion in MS-DW data using the
proposed method. The performance is comparable and better in certain cases than
conventional phase-based methods.
  Conclusion: The proposed method can achieve effective unaliasing of
fully/under-sampled MS-DW images without using explicit phase estimates.
