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.National Institute for Biomedical Imaging and Bioengineering (U.S.) (Grant NIBIB K99EB012107)National Institutes of Health (U.S.) (Grant NIH R01 EB007942)National Institute for Biomedical Imaging and Bioengineering (U.S.) (Grant NIBIB R01EB006847)Grant K99/R00 EB008129National Center for Research Resources (U.S.) (Grant NCRR P41RR14075)National Institutes of Health (U.S.) (Blueprint for Neuroscience Research U01MH093765)Siemens CorporationSiemens-MIT AllianceMIT-Center for Integration of Medicine and Innovative Technology (Medical Engineering Fellowship
