@article{LoktyushinESS2018,
  title = {{Autofocusing-based phase correction}},
  journal = {{Magnetic Resonance in Medicine}},
  abstract = {{Purpose Phase artifacts due to B0 inhomogeneity can severely degrade the quality of MR images. The artifacts are particularly prominent in long-TE scans and usually appear as ghosting and blur. We propose a retrospective phase correction method based on autofocusing. The proposed method uses raw data acquired with standard imaging sequences, and does not rely on navigators or external measures of field inhomogeneity. Methods We formulate and solve the optimization problem, where we seek the latent phase offsets that are associated with an optimal value of the image quality measure that is evaluated in the spatial domain. As a quality measure we use entropy computed on spatial image gradients. We propose two types of objective function, both compatible with parallel imaging and accelerated image acquisition. Results We evaluate the method on both synthetic and real data. In real data case we evaluate the performance on a range of sequences and images acquired with different acceleration factors. The experimental results demonstrate that our method is capable of minimizing ghosting artifacts and that the quality of the output images is similar to navigator-based reconstructions. Conclusion The presented technique can be alternative to or complement navigator-based methods, and is able to improve images with severe phase artifacts from all standard imaging sequences.}},
  volume = {80},
  number = {3},
  pages = {958--968},
  publisher = {Wiley-Liss},
  address = {New York},
  year = {2018},
  slug = {loktyushiness2018},
  author = {Loktyushin, A and Ehses, P and Sch\"olkopf, B and Scheffler, K}
}