  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.
