MR-STAT is a framework for obtaining multi-parametric quantitative MR maps using data from single short scans. A large-scale optimization problem is solved in which spatial localisation of signal and estimation of tissue parameters are performed simultaneously by directly fitting a Bloch-based volumetric signal model to the time domain data. In the current work, we exploit sparsity that is inherently present in the problem when using Cartesian sampling strategies to achieve an order of magnitude acceleration in reconstruction times. The new method is tested on synthetically generated data and on in-vivo brain data.
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