title: Fast iterative algorithm for the reconstruction of multishot non-cartesian diffusion data.
abstract: OBJECTIVE
  To accelerate the motion-compensated iterative reconstruction of multishot non-Cartesian diffusion data.
  
  
  METHODS
  The motion-compensated recovery of multishot non-Cartesian diffusion data is often performed using a modified iterative sensitivity-encoded algorithm. Specifically, the encoding matrix is replaced with a combination of nonuniform Fourier transforms and composite sensitivity functions, which account for the motion-induced phase errors. The main challenge with this scheme is the significantly increased computational complexity, which is directly related to the total number of composite sensitivity functions (number of shots × number of coils). The dimensionality of the composite sensitivity functions and hence the number of Fourier transforms within each iteration is reduced using a principal component analysis-based scheme. Using a Toeplitz-based conjugate gradient approach in combination with an augmented Lagrangian optimization scheme, a fast algorithm is proposed for the sparse recovery of diffusion data.
  
  
  RESULTS
  The proposed simplifications considerably reduce the computation time, especially in the recovery of diffusion data from under-sampled reconstructions using sparse optimization. By choosing appropriate number of basis functions to approximate the composite sensitivities, faster reconstruction (close to 9 times) with effective motion compensation is achieved.
  
  
  CONCLUSIONS
  The proposed enhancements can offer fast motion-compensated reconstruction of multishot diffusion data for arbitrary k-space trajectories.
authors.affiliation: Department of Electrical and Computer Engineering, University of Rochester, NewYork, USA.
authors.forename: Merry
authors.initials: M
authors.lastname: Mani
authors.affiliation: Department of Electrical and Computer Engineering, University of Iowa, Iowa, USA.
authors.forename: Mathews
authors.initials: M
authors.lastname: Jacob
authors.affiliation: Department of Radiology, University of Iowa, Iowa, USA.
authors.forename: Vincent
authors.initials: V
authors.lastname: Magnotta
authors.affiliation: Department of Biomedical Engineering, University of Rochester, NewYork, USA.
authors.forename: Jianhui
authors.initials: J
authors.lastname: Zhong
mesh_terms: D000328:Adult; D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D025341:Principal Component Analysis; D015203:Reproducibility of Results
keywords: Toeplitz-embedding; augmented Lagrangian; motion-compensated diffusion imaging; multishot diffusion imaging; principal component analysis; under-sampled reconstruction for high resolution diffusion imaging