BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Divergence-Free Wavelet Frames

E. Bostan, M. Unser, J.P. Ward

2015 Twenty-Second IEEE International Conference on Image Processing (ICIP'15), Québec QC, Canada, September 27-30, 2015, paper no. TEC-P19.2.

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets retain the basic characteristics (decay rate and order of vanishing moments) of the initial wavelets. Since the Leray projector is also shift-invariant, it is defined as a Fourier multiplier, and our construction is implemented efficiently using the fast Fourier transform. In order to illustrate the practicality of the method, we present vector field denoising experiments.

This abstract was originally published as E. Bostan, M. Unser, J.P. Ward, "Divergence-Free Wavelet Frames," IEEE Signal Processing Letters, vol. 22, no. 8, pp. 1142-1145, August 2015. 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/bostan1503.html,
AUTHOR="Bostan, E. and Unser, M. and Ward, J.P.",
TITLE="Divergence-Free Wavelet Frames",
BOOKTITLE="2015 Twenty-Second {IEEE} International Conference on Image
	Processing ({ICIP'15})",
YEAR="2015",
editor="",
volume="",
series="",
pages="",
address="Qu{\'{e}}bec QC, Canada",
month="September 27-30,",
organization="",
publisher="",
note="paper no.\ TEC-P19.2")
© 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.