  Magnetic resonance fingerprinting (MRF) can successfully recover quantitative
multi-parametric maps of human tissue in a very short acquisition time. Due to
their pseudo-random nature, the large spatial undersampling artifacts can be
filtered out by an exhaustive search over a pre-computed dictionary of signal
fingerprints. This reconstruction approach is robust to large data-model
discrepancies and is easy to implement. The curse of dimensionality and the
intrinsic rigidity of such a precomputed dictionary approach can however limit
its practical applicability. In this work, a method is presented to reconstruct
balanced gradient-echo (GRE) acquisitions with established iterative algorithms
for nonlinear least-squares, thus bypassing the dictionary computation and the
exhaustive search. The global convergence of the iterative approach is
investigated by studying the transient dynamic response of balanced GRE
sequences and its effect on the minimization landscape. Experimental design
criteria are derived which enforce sensitivity to the parameters of interest
and successful convergence. The method is validated on simulated and
experimentally acquired MRI data. Keywords: MR Fingerprinting, quantitative
MRI, Bloch equation, nonlinear least squares, sequence design.
