Low Rank Alternating Direction Method of Multipliers Reconstruction for   MR Fingerprinting
  Purpose   The proposed reconstruction framework addresses the reconstruction accuracy, noise propagation and computation time for Magnetic Resonance Fingerprinting (MRF).   Methods   Based on a singular value decomposition (SVD) of the signal evolution, MRF is formulated as a low rank inverse problem in which one image is reconstructed for each singular value under consideration. This low rank approximation of the signal evolution reduces the computational burden by reducing the number of Fourier transformations. Also, the low rank approximation improves the conditioning of the problem, which is further improved by extending the low rank inverse problem to an augmented Lagrangian that is solved by the alternating direction method of multipliers (ADMM). The root mean square error and the noise propagation are analyzed in simulations. For verification, in vivo examples are provided.   Results   The proposed low rank ADMM approach shows a reduced root mean square error compared to the original fingerprinting reconstruction, to a low rank approximation alone and to an ADMM approach without a low rank approximation. Incorporating sensitivity encoding allows for further artifact reduction.   Conclusion   The proposed reconstruction provides robust convergence, reduced computational burden and improved image quality compared to other MRF reconstruction approaches evaluated in this study. 
Jakob Assl\"ander, Martijn A Cloos, Florian Knoll, Daniel K Sodickson,   J\"urgen Hennig, Riccardo Lattanzi
physics.med-ph