title: Practical considerations for in vivo MRI with higher dimensional spatial encoding.
abstract: OBJECTIVE
  This work seeks to examine practical aspects of in vivo imaging when spatial encoding is performed with three or more encoding channels for a 2D image.
  
  
  METHODS
  The recently developed 4-Dimensional Radial In/Out (4D-RIO) trajectory is compared in simulations to an alternative higher-order encoding scheme referred to as O-space imaging. Direct comparison of local k-space representations leads to the proposal of a modification to the O-space imaging trajectory based on a scheme of prephasing to improve the reconstructed image quality. Data were collected using a 4D-RIO acquisition in vivo in the human brain and several image reconstructions were compared, exploiting the property that the dense encoding matrix, after a 1D or 2D Fourier transform, can be approximated by a sparse matrix by discarding entries below a chosen magnitude.
  
  
  RESULTS
  The proposed prephasing scheme for the O-space trajectory shows a marked improvement in quality in the simulated image reconstruction. In experiments, 4D-RIO data acquired in vivo in the human brain can be reconstructed to a reasonable quality using only 5 % of the encoding matrix--massively reducing computer memory requirements for a practical reconstruction.
  
  
  CONCLUSIONS
  Trajectory design and reconstruction techniques such as these may prove especially useful when extending generalized higher-order encoding methods to 3D images.
authors.affiliation: University Medical Center Freiburg, Freiburg, Germany. daniel.gallichan@epfl.ch
authors.forename: Daniel
authors.initials: D
authors.lastname: Gallichan
authors.forename: Chris A
authors.initials: CA
authors.lastname: Cocosco
authors.forename: Gerrit
authors.initials: G
authors.lastname: Schultz
authors.forename: Hans
authors.initials: H
authors.lastname: Weber
authors.forename: Anna M
authors.initials: AM
authors.lastname: Welz
authors.forename: Jürgen
authors.initials: J
authors.lastname: Hennig
authors.forename: Maxim
authors.initials: M
authors.lastname: Zaitsev
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001921:Brain / Q000473:pathology; D002138:Calibration; D003198:Computer Simulation; D003201:Computers; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D015233:Models, Statistical; D012984:Software