Fast image reconstruction with L2-regularization

J Magn Reson Imaging. 2014 Jul;40(1):181-91. doi: 10.1002/jmri.24365. Epub 2013 Nov 4.


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.

Keywords: diffusion imaging; lipid suppression; regularization; spectroscopic imaging; susceptibility mapping.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms*
  • Brain / anatomy & histology*
  • Humans
  • Image Enhancement / methods*
  • Image Interpretation, Computer-Assisted / methods*
  • Magnetic Resonance Imaging / instrumentation
  • Magnetic Resonance Imaging / methods*
  • Numerical Analysis, Computer-Assisted
  • Phantoms, Imaging
  • Reproducibility of Results
  • Sensitivity and Specificity
  • Signal Processing, Computer-Assisted*