Fast quantitative MRI as a nonlinear tomography problem.

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.