title: Low rank alternating direction method of multipliers reconstruction for MR fingerprinting.
abstract: OBJECTIVE
  The proposed reconstruction framework addresses the reconstruction accuracy, noise propagation and computation time for magnetic resonance fingerprinting.
  
  
  METHODS
  Based on a singular value decomposition of the signal evolution, magnetic resonance fingerprinting is formulated as a low rank (LR) inverse problem in which one image is reconstructed for each singular value under consideration. This LR approximation of the signal evolution reduces the computational burden by reducing the number of Fourier transformations. Also, the LR approximation improves the conditioning of the problem, which is further improved by extending the LR inverse problem to an augmented Lagrangian that is solved by the alternating direction method of multipliers. The root mean square error and the noise propagation are analyzed in simulations. For verification, in vivo examples are provided.
  
  
  RESULTS
  The proposed LR alternating direction method of multipliers approach shows a reduced root mean square error compared to the original fingerprinting reconstruction, to a LR approximation alone and to an alternating direction method of multipliers approach without a LR approximation. Incorporating sensitivity encoding allows for further artifact reduction.
  
  
  CONCLUSIONS
  The proposed reconstruction provides robust convergence, reduced computational burden and improved image quality compared to other magnetic resonance fingerprinting reconstruction approaches evaluated in this study. Magn Reson Med 79:83-96, 2018. © 2017 International Society for Magnetic Resonance in Medicine.
authors.affiliation: Department of Radiology, New York University School of Medicine, Bernard and Irene Schwartz Center for Biomedical Imaging, New York, New York, USA.|Department of Radiology, New York University School of Medicine, Center for Advanced Imaging Innovation and Research (CAI2R), New York, New York, USA.|Department of Radiology, Medical Physics, Medical Center, University of Freiburg, Faculty of Medicine, University of Freiburg, Freiburg, Germany.
authors.forename: Jakob
authors.initials: J
authors.lastname: Assländer
authors.affiliation: Department of Radiology, New York University School of Medicine, Bernard and Irene Schwartz Center for Biomedical Imaging, New York, New York, USA.|Department of Radiology, New York University School of Medicine, Center for Advanced Imaging Innovation and Research (CAI2R), New York, New York, USA.
authors.forename: Martijn A
authors.initials: MA
authors.lastname: Cloos
authors.affiliation: Department of Radiology, New York University School of Medicine, Bernard and Irene Schwartz Center for Biomedical Imaging, New York, New York, USA.|Department of Radiology, New York University School of Medicine, Center for Advanced Imaging Innovation and Research (CAI2R), New York, New York, USA.
authors.forename: Florian
authors.initials: F
authors.lastname: Knoll
authors.affiliation: Department of Radiology, New York University School of Medicine, Bernard and Irene Schwartz Center for Biomedical Imaging, New York, New York, USA.|Department of Radiology, New York University School of Medicine, Center for Advanced Imaging Innovation and Research (CAI2R), New York, New York, USA.
authors.forename: Daniel K
authors.initials: DK
authors.lastname: Sodickson
authors.affiliation: Department of Radiology, Medical Physics, Medical Center, University of Freiburg, Faculty of Medicine, University of Freiburg, Freiburg, Germany.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Hennig
authors.affiliation: Department of Radiology, New York University School of Medicine, Bernard and Irene Schwartz Center for Biomedical Imaging, New York, New York, USA.|Department of Radiology, New York University School of Medicine, Center for Advanced Imaging Innovation and Research (CAI2R), New York, New York, USA.
authors.forename: Riccardo
authors.initials: R
authors.lastname: Lattanzi
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001921:Brain / Q000000981:diagnostic imaging; D001931:Brain Mapping; D003198:Computer Simulation; D044962:Data Compression / Q000379:methods; D005583:Fourier Analysis; D064368:Healthy Volunteers; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D060526:Magnetic Fields; D008279:Magnetic Resonance Imaging; D015233:Models, Statistical; D019047:Phantoms, Imaging; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted
keywords: MRF; SVD; augmented Lagrangian; parallel imaging; parameter mapping; quantitative MRI