  Quantitative Magnetic Resonance Imaging (MRI) is based on a two-steps
approach: estimation of the magnetic moments distribution inside the body,
followed by a voxel-by-voxel quantification of the human tissue properties.
This splitting simplifies the computations but poses several constraints on the
measurement process, limiting its efficiency. Here, we perform quantitative MRI
as a one step process; signal localization and parameter quantification are
simultaneously obtained by the solution of a large scale nonlinear inversion
problem based on first-principles. As a consequence, the constraints on the
measurement process can be relaxed and acquisition schemes that are time
efficient and widely available in clinical MRI scanners can be employed. We
show that the nonlinear tomography approach is applicable to MRI and returns
human tissue maps from very short experiments. Keywords: MR-STAT, quantitative
MRI, nonlinear tomography, MR Fingerprinting, large scale inversion.
