title: MR image reconstruction from generalized projections.
abstract: OBJECTIVE
  Currently, the time required for image reconstruction is prohibitively long if data are acquired using multidimensional imaging trajectories that make use of multichannel systems equipped with nonlinear gradients. Methods are presented that reduce the computational complexity of the iterative time-domain reconstruction algorithm down from O(N(4)) to O(N(3)).
  
  
  BACKGROUND
  For generalized projections, a large class of multidimensional imaging trajectories, the encoding matrix can be focused to sparse bands by introducing an appropriate filter function along the frequency-encoding direction. The reconstruction can be speeded up by ignoring values below a predefined threshold level.
  
  
  METHODS
  Two methods are presented that differ in how the filter is incorporated into the reconstruction algorithm. The first method represents, without implementation of a threshold, a weighted version of the time-domain method, while the second method is equivalent to it.
  
  
  RESULTS
  Simulation and measurement results show that image reconstruction from high-resolution imaging data can be speeded up by up to two orders of magnitude. While the weighted reconstruction requires more iterations to reach an optimum than the second method, it is less sensitive to thresholding.
  
  
  CONCLUSIONS
  For complex spatial encoding strategies that involve nonlinear gradient fields, fast and accurate image reconstruction methods are provided that are particularly efficient for high-resolution anatomical imaging.
authors.affiliation: Medical Physics, Department of Radiology, University Medical Center Freiburg, Freiburg, Germany.
authors.forename: Gerrit
authors.initials: G
authors.lastname: Schultz
authors.forename: Daniel
authors.initials: D
authors.lastname: Gallichan
authors.forename: Marco
authors.initials: M
authors.lastname: Reisert
authors.forename: Jürgen
authors.initials: J
authors.lastname: Hennig
authors.forename: Maxim
authors.initials: M
authors.lastname: Zaitsev
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000295:instrumentation / Q000379:methods*; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: PatLoc; gradient; magnetic resonance imaging; nonlinear; projections; reconstruction