Fast image reconstruction with L2‐regularization. Issue 1 (4th November 2013) - Bilgic, Berkin; Chatnuntawech, Itthi; Fan, Audrey P.; Setsompop, Kawin; Cauley, Stephen F.; Wald, Lawrence L.; Adalsteinsson, Elfar
<x xml:space="preserve">Abstract</x> 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. J. Magn. Reson. Imaging 2014;40:181–191 © 2013 Wiley Periodicals, Inc.