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International Journal of Biomedical Imaging
Volume 2007 (2007), Article ID 24727, 9 pages
Research Article

A Note on the Iterative MRI Reconstruction from Nonuniform k-Space Data

1Institute of Mathematics, University of Lübeck, Lübeck 23538, Germany
2Department of Mathematics, Chemnitz University of Technology, Chemnitz 09107, Germany

Received 18 January 2006; Revised 7 November 2006; Accepted 16 January 2007

Academic Editor: David L. Wilson

Copyright © 2007 Tobias Knopp et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In magnetic resonance imaging (MRI), methods that use a non-Cartesian grid in k-space are becoming increasingly important. In this paper, we use a recently proposed implicit discretisation scheme which generalises the standard approach based on gridding. While the latter succeeds for sufficiently uniform sampling sets and accurate estimated density compensation weights, the implicit method further improves the reconstruction quality when the sampling scheme or the weights are less regular. Both approaches can be solved efficiently with the nonequispaced FFT. Due to several new techniques for the storage of an involved sparse matrix, our examples include also the reconstruction of a large 3D data set. We present four case studies and report on efficient implementation of the related algorithms.