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MR‐STAT is a recently proposed framework that allows the reconstruction of multiple quantitative parameter maps from a single short scan by performing spatial localisation and parameter estimation on the time‐domain data simultaneously, without relying on the fast Fourier transform (FFT). To do this at high resolution, specialized algorithms are required to solve the underlying large‐scale nonlinear optimisation problem. We propose a matrix‐free and parallelized inexact Gauss–Newton based reconstruction algorithm for this purpose. The proposed algorithm is implemented on a high‐performance computing cluster and is demonstrated to be able to generate high‐resolution (1 mm   ×   1 mm in‐plane resolution) quantitative parameter maps in simulation, phantom, and in vivo brain experiments. ReconstructedT    1andT    2values for the gel phantoms are in agreement with results from gold standard measurements and, for the in vivo experiments, the quantitative values show good agreement with literature values. In all experiments, short pulse sequences with robust Cartesian sampling are used, for which MR fingerprinting reconstructions are shown to fail.

High‐resolution in vivo MR‐STAT using a matrix‐free and parallelized reconstruction algorithm