  In quantitative Magnetic Resonance Imaging, traditional methods suffer from
the so-called Partial Volume Effect (PVE) due to spatial resolution
limitations. As a consequence of PVE, the parameters of the voxels containing
more than one tissue are not correctly estimated. Magnetic Resonance
Fingerprinting (MRF) is not an exception. The existing methods addressing PVE
are neither scalable nor accurate. We propose to formulate the recovery of
multiple tissues per voxel as a nonconvex constrained least-squares
minimisation problem. To solve this problem, we develop a memory efficient,
greedy approximate projected gradient descent algorithm, dubbed GAP-MRF. Our
method adaptively finds the regions of interest on the manifold of fingerprints
defined by the MRF sequence. We generalise our method to compensate for phase
errors appearing in the model, using an alternating minimisation approach. We
show, through simulations on synthetic data with PVE, that our algorithm
outperforms state-of-the-art methods. Our approach is validated on the EUROSPIN
phantom and on in vivo datasets.

Image and Video Processing