Greedy techniques for magnetic resonance fingerprinting

Abstract

In this manuscript, we show four main results in the context of Magnetic Resonance Fingerprinting (MRF): • 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 vivo datasets. 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 sensitivity maps.