|dc.description.abstract||In this manuscript, we show four main results in the context of Magnetic Resonance
• A memory efficient method to explore the manifold of fingerprints.
• A method that allows super-resolution reconstructions relying on spatial regularisation.
• An extension to partial volumes and a greedy approximate projection algorithm.
• An extension to Self-Calibration and Imaging.
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. 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 non-convex 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 in reconstruction quality. Our approach is validated on the EUROSPIN phantom and on in
Coil sensitivity calibration is a crucial step in the reconstruction process to obtain
accurate results. Usual MRI self-calibration methods, reconstructing independently
the time acquisitions, are not suitable for highly undersampled MRF data. In this
work, leveraging recent developments in non-convex optimisation, we propose the first
self-calibration method for MRF, exploiting the correlation in the time acquisitions, the spatial regularity of the magnetisation images and the smoothness of the coil