title: Fast image reconstruction with L2-regularization.
abstract: OBJECTIVE
  We introduce L2-regularized reconstruction algorithms with closed-form solutions that achieve dramatic computational speed-up relative to state of the art L1- and L2-based iterative algorithms while maintaining similar image quality for various applications in MRI reconstruction.
  
  
  METHODS
  We compare fast L2-based methods to state of the art algorithms employing iterative L1- and L2-regularization in numerical phantom and in vivo data in three applications; (i) Fast Quantitative Susceptibility Mapping (QSM), (ii) Lipid artifact suppression in Magnetic Resonance Spectroscopic Imaging (MRSI), and (iii) Diffusion Spectrum Imaging (DSI). In all cases, proposed L2-based methods are compared with the state of the art algorithms, and two to three orders of magnitude speed up is demonstrated with similar reconstruction quality.
  
  
  RESULTS
  The closed-form solution developed for regularized QSM allows processing of a three-dimensional volume under 5 s, the proposed lipid suppression algorithm takes under 1 s to reconstruct single-slice MRSI data, while the PCA based DSI algorithm estimates diffusion propagators from undersampled q-space for a single slice under 30 s, all running in Matlab using a standard workstation.
  
  
  CONCLUSIONS
  For the applications considered herein, closed-form L2-regularization can be a faster alternative to its iterative counterpart or L1-based iterative algorithms, without compromising image quality.
authors.affiliation: Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA; A. A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, Massachusetts, USA.
authors.forename: Berkin
authors.initials: B
authors.lastname: Bilgic
authors.forename: Itthi
authors.initials: I
authors.lastname: Chatnuntawech
authors.forename: Audrey P
authors.initials: AP
authors.lastname: Fan
authors.forename: Kawin
authors.initials: K
authors.lastname: Setsompop
authors.forename: Stephen F
authors.initials: SF
authors.lastname: Cauley
authors.forename: Lawrence L
authors.initials: LL
authors.lastname: Wald
authors.forename: Elfar
authors.initials: E
authors.lastname: Adalsteinsson
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000295:instrumentation / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D019047:Phantoms, Imaging; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted
keywords: diffusion imaging; lipid suppression; regularization; spectroscopic imaging; susceptibility mapping