EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > MRI Reconstruction


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance Imaging

M. Guerquin-Kern, M. Häberlin, K.P. Pruessmann, M. Unser

IEEE Transactions on Medical Imaging, vol. 30, no. 9, pp. 1649-1660, September 2011.



In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space trajectories. Reconstruction is posed as an optimization problem that could be solved with the iterative shrinkage/thresholding algorithm (ISTA) which, unfortunately, converges slowly. To make the approach more practical, we propose a variant that combines recent improvements in convex optimization and that can be tuned to a given specific k-space trajectory. We present a mathematical analysis that explains the performance of the algorithms. Using simulated and in vivo data, we show that our nonlinear method is fast, as it accelerates ISTA by almost two orders of magnitude. We also show that it remains competitive with TV regularization in terms of image quality.

Erratum

  • p. 1653, first column, Algorithm 3, update of v, the division bar is misplaced. The corrected equation should read vn+1wn+1 + (tn+1 − 1) (wn+1wn) ⁄ tn;


@ARTICLE(http://bigwww.epfl.ch/publications/guerquinkern1102.html,
AUTHOR="Guerquin-Kern, M. and H{\"{a}}berlin, M. and Pruessmann, K.P.
        and Unser, M.",
TITLE="A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance
        Imaging",
JOURNAL="{IEEE} Transactions on Medical Imaging",
YEAR="2011",
volume="30",
number="9",
pages="1649--1660",
month="September",
note="")

© 2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.