  Purpose: Magnetic Resonance Fingerprinting (MRF) is a relatively new approach
that provides quantitative MRI measures using randomized acquisition.
Extraction of physical quantitative tissue parameters is performed off-line,
without the need of patient presence, based on acquisition with varying
parameters and a dictionary generated according to the Bloch equation
simulations. MRF uses hundreds of radio frequency (RF) excitation pulses for
acquisition, and therefore a high undersampling ratio in the sampling domain
(k-space) is required for reasonable scanning time. This undersampling causes
spatial artifacts that hamper the ability to accurately estimate the tissue's
quantitative values. In this work, we introduce a new approach for quantitative
MRI using MRF, called magnetic resonance Fingerprinting with LOw Rank (FLOR).
  Methods: We exploit the low rank property of the concatenated temporal
imaging contrasts, on top of the fact that the MRF signal is sparsely
represented in the generated dictionary domain. We present an iterative scheme
that consists of a gradient step followed by a low rank projection using the
singular value decomposition.
  Results: Experimental results consist of retrospective sampling, that allows
comparison to a well defined reference, and prospective sampling that shows the
performance of FLOR for a real-data sampling scenario. Both experiments
demonstrate improved parameter accuracy compared to other compressed-sensing
and low-rank based methods for MRF at 5% and 9% sampling ratios, for the
retrospective and prospective experiments, respectively.
  Conclusions: We have shown through retrospective and prospective experiments
that by exploiting the low rank nature of the MRF signal, FLOR recovers the MRF
temporal undersampled images and provides more accurate parameter maps compared
to previous iterative methods.
