On the Temporal Fidelity of Nonlinear Inverse Reconstructions for Real- Time MRI – The Motion Challenge

Jens Frahm1, 2, *, Sebastian Schätz1, Markus Untenberger1, Shuo Zhang1, 2, Dirk Voit1, K. Dietmar Merboldt1, Jan M. Sohns2, 3, Joachim Lotz2, 3, Martin Uecker4
1 Biomedizinische NMR Forschungs GmbH am MPI für biophysikalische Chemie, 37070 Göttingen, Germany
2 DZHK (German Cardiovascular Research Center), partner site Göttingen
3 Diagnostische und Interventionelle Radiologie, Universitätsmedizin Göttingen, 37075 Göttingen, Germany
4 Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA

© 2014 Frahm et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Biomedizinische NMR Forschungs GmbH am Max-Planck-Institut für biophysikalische Chemie, 37070 Göttingen, Germany; Tel: +49-551-201-1721; Fax: +49-551-201-1307; E-mail:



To evaluate the temporal accuracy of a self-consistent nonlinear inverse reconstruction method (NLINV) for real-time MRI using highly undersampled radial gradient-echo sequences and to present an open source framework for the motion assessment of real-time MRI methods.


Serial image reconstructions by NLINV combine a joint estimation of individual frames and corresponding coil sensitivities with temporal regularization to a preceding frame. The temporal fidelity of the method was determined with a phantom consisting of water-filled tubes rotating at defined angular velocity. The conditions tested correspond to real-time cardiac MRI using SSFP contrast at 1.5 T (40 ms resolution) and T1 contrast at 3.0 T (33 ms and 18 ms resolution). In addition, the performance of a post-processing temporal median filter was evaluated.


NLINV reconstructions without temporal filtering yield accurate estimations as long as the speed of a small moving object corresponds to a spatial displacement during the acquisition of a single frame which is smaller than the object itself. Faster movements may lead to geometric distortions. For small objects moving at high velocity, a median filter may severely compromise the spatiotemporal accuracy.


NLINV reconstructions offer excellent temporal fidelity as long as the image acquisition time is short enough to adequately sample (“freeze”) the object movement. Temporal filtering should be applied with caution. The motion framework emerges as a valuable tool for the evaluation of real-time MRI methods.

Keywords: Real-time MRI, Radial MRI, Iterative reconstruction, Temporal fidelity.