title: PCLR: phase-constrained low-rank model for compressive diffusion-weighted MRI.
abstract: OBJECTIVE
  This work develops a compressive sensing approach for diffusion-weighted (DW) MRI.
  
  
  METHODS
  A phase-constrained low-rank (PCLR) approach was developed using the image coherence across the DW directions for efficient compressive DW MRI, while accounting for drastic phase changes across the DW directions, possibly as a result of eddy current, and rigid and nonrigid motions. In PCLR, a low-resolution phase estimation was used for removing phase inconsistency between DW directions. In our implementation, GRAPPA (generalized autocalibrating partial parallel acquisition) was incorporated for better phase estimation while allowing higher undersampling factor. An efficient and easy-to-implement image reconstruction algorithm, consisting mainly of partial Fourier update and singular value decomposition, was developed for solving PCLR.
  
  
  RESULTS
  The error measures based on diffusion-tensor-derived metrics and tractography indicated that PCLR, with its joint reconstruction of all DW images using the image coherence, outperformed the frame-independent reconstruction through zero-padding FFT. Furthermore, using GRAPPA for phase estimation, PCLR readily achieved a four-fold undersampling.
  
  
  CONCLUSIONS
  The PCLR is developed and demonstrated for compressive DW MRI. A four-fold reduction in k-space sampling could be readily achieved without substantial degradation of reconstructed images and diffusion tensor measures, making it possible to significantly reduce the data acquisition in DW MRI and/or improve spatial and angular resolutions.
authors: Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322.|Department of Radiology and Imaging Sciences, Emory University, Atlanta, GA 30322.
authors: Hao
authors: H
authors: Gao
authors: Marcus Autism Center, Department of Pediatrics, Emory University, Atlanta, GA 30322.
authors: Longchuan
authors: L
authors: Li
authors: Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322.
authors: Kai
authors: K
authors: Zhang
authors: Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322.
authors: Weifeng
authors: W
authors: Zhou
authors: The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology / Emory University, Atlanta, GA 30322.
authors: Xiaoping
authors: X
authors: Hu
mesh_terms: D000465:Algorithms; D001931:Brain Mapping / Q000379:methods*; D038524:Diffusion Magnetic Resonance Imaging / Q000379:methods*; D056324:Diffusion Tensor Imaging / Q000379:methods; D064368:Healthy Volunteers; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008297:Male
keywords: GRAPPA; compressive sensing; diffusion tensor; diffusion-weighted MRI; low rank; phase correction; tractography