Recent Advances in Acquisition/Reconstruction Algorithms for Undersampled Magnetic Resonance Imaging

Several applications of Magnetic Resonance Imaging (MRI), in particular dynamic MRI and functional MRI (fMRI), require rapid acquisition to measure dynamic processes changes. Experimental data are collected in the k-space by following different trajectories to cover the whole space. Complete data acquisition necessitates waiting for a fixed time interval: a reduced number of collected trajectories allows acquisition time reduction but undersampling occurs, often producing artifacts. In what follows, a review of methods for sparse sampling acquisition and reconstruction is presented. In particular, a differentiation is done between sparse acquisition methods which do not use any restoration algorithm (artifacts are tolerated) and those methods for which a restoration algorithm is essential. The first class contains also methods where spatial information is shared between temporal images to reduce the collected data. In the second class of methods, a differentiation is done between those reconstruction/restoration methods that reduce artifacts independently of the sample shape, and those restoration methods that adapt their action by modifying the acquisition trajectories during the acquisition, i.e. the chosen trajectories (both in number and directions) are dependent on the sample shape. A third emerging class of methods, those including hybrid forms of the second class, are also reported