MR-STAT is a framework for obtaining multiple quantitative parameter maps from a very short scan. The parameter maps are obtained by fitting a Bloch-based signal model directly to the time domain data. No Fourier transform is needed. In this work we demonstrate that MR-STAT can obtain excellent high-resolution in-vivo quantitative maps using very short Cartesian acquisitions standardly available on clinical MR systems. The solution of the large-scale reconstruction problem is made possible by a highly parallelized, limited-memory algorithm.