Fast image reconstruction with L2-regularization

Berkin Bilgic, Itthi Chatnuntawech, Audrey P. Fan, Kawin Setsompop, Stephen F. Cauley, Lawrence L. Wald, Elfar Adalsteinsson

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


Purpose 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. Materials and 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. Conclusion 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.

Original languageEnglish (US)
Pages (from-to)181-191
Number of pages11
JournalJournal of Magnetic Resonance Imaging
Issue number1
StatePublished - Jul 2014
Externally publishedYes


  • diffusion imaging
  • lipid suppression
  • regularization
  • spectroscopic imaging
  • susceptibility mapping

ASJC Scopus subject areas

  • Radiology Nuclear Medicine and imaging


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