EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Variational Denoising


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

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

E. Bostan, S. Lefkimmiatis, O. Vardoulis, N. Stergiopulos, M. Unser

IEEE Signal Processing Letters, vol. 22, no. 6, pp. 762-766, June 2015.



We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our method is invariant with respect to fundamental transformations and can be efficiently solved. We conduct numerical experiments on several phantom data and report improved performance compared to existing vectorial extensions of total variation and curl-divergence regularizations. Finally, we apply our reconstruction method to an experimentally-acquired phase-contrast MRI recording for enhancing the data visualization.

Supplementary material

  • Supplementary Note (PDF file) (139 Kb). Proof that the TVp regularizers are invariant under translation, scaling (up to a multiplicative factor), and rotation.

@ARTICLE(http://bigwww.epfl.ch/publications/bostan1501.html,
AUTHOR="Bostan, E. and Lefkimmiatis, S. and Vardoulis, O. and
        Stergiopulos, N. and Unser, M.",
TITLE="Improved Variational Denoising of Flow Fields with Application to
        Phase-Contrast {MRI} Data",
JOURNAL="{IEEE} Signal Processing Letters",
YEAR="2015",
volume="22",
number="6",
pages="762--766",
month="June",
note="")

© 2015 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.