A Note on the Iterative MRI Reconstruction from Nonuniform <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math>-Space Data

Knopp, Tobias; Kunis, Stefan; Potts, Daniel

doi:https://doi.org/10.1155/2007/24727

International Journal of Biomedical Imaging

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Research Article | Open Access

Volume 2007 | Article ID 024727 | https://doi.org/10.1155/2007/24727

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

Tobias Knopp,¹Stefan Kunis,²and Daniel Potts²

Academic Editor: David L. Wilson

Received18 Jan 2006

Revised07 Nov 2006

Accepted16 Jan 2007

Published13 Mar 2007

Abstract

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.

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Copyright

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.

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