title: SC-GRAPPA: Self-constraint noniterative GRAPPA reconstruction with closed-form solution.
abstract: OBJECTIVE
  Parallel MRI (pMRI) reconstruction techniques are commonly used to reduce scan time by undersampling the k-space data. GRAPPA, a k-space based pMRI technique, is widely used clinically because of its robustness. In GRAPPA, the missing k-space data are estimated by solving a set of linear equations; however, this set of equations does not take advantage of the correlations within the missing k-space data. All k-space data in a neighborhood acquired from a phased-array coil are correlated. The correlation can be estimated easily as a self-constraint condition, and formulated as an extra set of linear equations to improve the performance of GRAPPA. The authors propose a modified k-space based pMRI technique called self-constraint GRAPPA (SC-GRAPPA) which combines the linear equations of GRAPPA with these extra equations to solve for the missing k-space data. Since SC-GRAPPA utilizes a least-squares solution of the linear equations, it has a closed-form solution that does not require an iterative solver.
  
  
  METHODS
  The SC-GRAPPA equation was derived by incorporating GRAPPA as a prior estimate. SC-GRAPPA was tested in a uniform phantom and two normal volunteers. MR real-time cardiac cine images with acceleration rate 5 and 6 were reconstructed using GRAPPA and SC-GRAPPA.
  
  
  RESULTS
  SC-GRAPPA showed a significantly lower artifact level, and a greater than 10% overall signal-to-noise ratio (SNR) gain over GRAPPA, with more significant SNR gain observed in low-SNR regions of the images.
  
  
  CONCLUSIONS
  SC-GRAPPA offers improved pMRI reconstruction, and is expected to benefit clinical imaging applications in the future.
authors.affiliation: Davis Heart and Lung Research Institute, The Ohio State University, Columbus, OH, USA.
authors.forename: Yu
authors.initials: Y
authors.lastname: Ding
authors.forename: Hui
authors.initials: H
authors.lastname: Xue
authors.forename: Rizwan
authors.initials: R
authors.lastname: Ahmad
authors.forename: Samuel T
authors.initials: ST
authors.lastname: Ting
authors.forename: Orlando P
authors.initials: OP
authors.lastname: Simonetti
mesh_terms: D000465:Algorithms; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D019028:Magnetic Resonance Imaging, Cine / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity