title: Fast GRAPPA reconstruction with random projection.
abstract: OBJECTIVE
  To address the issue of computational complexity in generalized autocalibrating partially parallel acquisition (GRAPPA) when several calibration data are used.
  
  
  METHODS
  GRAPPA requires fully sampled data for accurate calibration with increasing data needed for higher reduction factors to maintain accuracy, which leads to longer computational time, especially in a three-dimensional (3D) setting and with higher channel count coils. Channel reduction methods have been developed to address this issue when massive array coils are used. In this study, the complexity problem was addressed from a different prospective. Instead of compressing to fewer channels, we propose the use of random projections to reduce the dimension of the linear equation in the calibration phase. The equivalence before and after the reduction is supported by the Johnson-Lindenstrauss lemma. The proposed random projection method can be integrated with channel reduction sequentially for even higher computational efficiency.
  
  
  RESULTS
  Experimental results show that GRAPPA with random projection can achieve comparable image quality with much less computational time when compared with conventional GRAPPA without random projection.
  
  
  CONCLUSIONS
  The proposed random projection method is able to reduce the computational time of GRAPPA, especially in a 3D setting, without compromising the image quality, or to improve the reconstruction quality by allowing more data for calibration when the computational time is a limiting factor. Magn Reson Med 74:71-80, 2015. © 2014 Wiley Periodicals, Inc.
authors.affiliation: Department of Biomedical Engineering, Department of Electrical Engineering, The State University of New York at Buffalo, Buffalo, New York, USA.
authors.forename: Jingyuan
authors.initials: J
authors.lastname: Lyu
authors.affiliation: Neuroimaging Research, Barrow Neurological Institute, Phoenix, Arizona, USA.
authors.forename: Yuchou
authors.initials: Y
authors.lastname: Chang
authors.affiliation: Department of Biomedical Engineering, Department of Electrical Engineering, The State University of New York at Buffalo, Buffalo, New York, USA.
authors.forename: Leslie
authors.initials: L
authors.lastname: Ying
keywords: GRAPPA; Johnson-Lindenstrauss lemma; auto-calibration; dimension reduction; random projection