  Purpose: To develop an algorithm for robust partial Fourier (PF)
reconstruction applicable to diffusion-weighted (DW) images with non-smooth
phase variations.
  Methods: Based on an unrolled proximal splitting algorithm, a neural network
architecture is derived which alternates between data consistency operations
and regularization implemented by recurrent convolutions. In order to exploit
correlations, multiple repetitions of the same slice are jointly reconstructed
under consideration of permutation-equivariance. The algorithm is trained on DW
liver data of 60 volunteers and evaluated on retrospectively and prospectively
sub-sampled data of different anatomies and resolutions.
  Results: The proposed method is able to significantly outperform conventional
PF techniques on retrospectively sub-sampled data in terms of quantitative
measures as well as perceptual image quality. In this context, joint
reconstruction of repetitions as well as the particular type of recurrent
network unrolling are found to be beneficial with respect to reconstruction
quality. On prospectively PF-sampled data, the proposed method enables DW
imaging with higher signal without sacrificing image resolution or introducing
additional artifacts. Alternatively, it can be used to counter the TE increase
in acquisitions with higher resolution. Further, generalizability can be shown
to prospective brain data exhibiting anatomies and contrasts not present in the
training set.
  Conclusion: This work demonstrates that robust PF reconstruction of DW data
is feasible even at strong PF factors in anatomies prone to phase variations.
Since the proposed method does not rely on smoothness priors of the phase but
uses learned recurrent convolutions instead, artifacts of conventional PF
methods can be avoided.
