  Magnetic resonance fingerprinting (MRF) is a technique for quantitative
estimation of spin-relaxation parameters from magnetic-resonance data. Most
current MRF approaches assume that only one tissue is present in each voxel,
which neglects the tissue's microstructure, and may lead to artifacts in the
recovered parameter maps at boundaries between tissues. In this work, we
propose a multicompartment MRF model that accounts for the presence of multiple
tissues per voxel. The model is fit to the data by iteratively solving a sparse
linear inverse problem at each voxel, in order to express the magnetization
signal as a linear combination of a few fingerprints in the precomputed
dictionary. Thresholding-based methods commonly used for sparse recovery and
compressed sensing do not perform well in this setting due to the high local
coherence of the dictionary. Instead, we solve this challenging sparse-recovery
problem by applying reweighted-l1-norm regularization, implemented using an
efficient interior-point method. The proposed approach is validated with
simulated data at different noise levels and undersampling factors, as well as
with a controlled phantom imaging experiment on a clinical magnetic-resonance
system.
