title: Paradoxical effect of the signal-to-noise ratio of GRAPPA calibration lines: A quantitative study.
abstract: OBJECTIVE
  Intuitively, GRAPPA auto-calibration signal (ACS) lines with higher signal-to-noise ratio (SNR) may be expected to boost the accuracy of kernel estimation and increase the SNR of GRAPPA reconstructed images. Paradoxically, Sodickson and his colleagues pointed out that using ACS lines with high SNR may actually lead to lower SNR in the GRAPPA reconstructed images. A quantitative study of how the noise in the ACS lines affects the SNR of the GRAPPA reconstructed images is presented.
  
  
  METHODS
  In a phantom, the singular values of the GRAPPA encoding matrix and the root-mean-square error of GRAPPA reconstruction were evaluated using multiple sets of ACS lines with variant SNR. In volunteers, ACS lines with high and low SNR were estimated, and the SNR of corresponding TGRAPPA reconstructed images was evaluated.
  
  
  RESULTS
  We show that the condition number of the GRAPPA kernel estimation equations is proportional to the SNR of the ACS lines. In dynamic image series reconstructed with TGRAPPA, high SNR ACS lines result in reduced SNR if appropriate regularization is not applied.
  
  
  CONCLUSIONS
  Noise has a similar effect to Tikhonov regularization. Without appropriate regularization, a GRAPPA kernel estimated from ACS lines with higher SNR amplifies random noise in the GRAPPA reconstruction. Magn Reson Med 74:231-239, 2015. © 2014 Wiley Periodicals, Inc.
authors: Dorothy M. Davis Heart and Lung Research Institute, The Ohio State University, Columbus, Ohio, USA.
authors: Yu
authors: Y
authors: Ding
authors: Magnetic Resonance Technology Program, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland, USA.
authors: Hui
authors: H
authors: Xue
authors: Dorothy M. Davis Heart and Lung Research Institute, The Ohio State University, Columbus, Ohio, USA.|Department of Electrical and Computer Engineering, The Ohio State University, Columbus, Ohio, USA.
authors: Rizwan
authors: R
authors: Ahmad
authors: Siemens Corporate Research, Princeton, New Jersey, USA.
authors: Ti-Chiun
authors: TC
authors: Chang
authors: Dorothy M. Davis Heart and Lung Research Institute, The Ohio State University, Columbus, Ohio, USA.|Department of Biomedical Engineering, The Ohio State University, Columbus, Ohio, USA.
authors: Samuel T
authors: ST
authors: Ting
authors: Dorothy M. Davis Heart and Lung Research Institute, The Ohio State University, Columbus, Ohio, USA.|Department of Biomedical Engineering, The Ohio State University, Columbus, Ohio, USA.|Department of Internal Medicine, The Ohio State University, Columbus, Ohio, USA.|Department of Radiology, The Ohio State University, Columbus, Ohio, USA.
authors: Orlando P
authors: OP
authors: Simonetti
keywords: GRAPPA; condition number; real-time MRI; signal to noise ratio