EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Wavelet Shrinkage


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

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Wavelet Shrinkage with Consistent Cycle Spinning Generalizes Total Variation Denoising

U. Kamilov, E. Bostan, M. Unser

IEEE Signal Processing Letters, vol. 19, no. 4, pp. 187-190, April 2012.



We introduce a new wavelet-based method for the implementation of Total-Variation-type denoising. The data term is least-squares, while the regularization term is gradient-based. The particularity of our method is to exploit a link between the discrete gradient and wavelet shrinkage with cycle spinning, which we express by using redundant wavelets. The redundancy of the representation gives us the freedom to enforce additional constraints (e.g., normalization) on the solution to the denoising problem. We perform optimization in an augmented-Lagrangian framework, which decouples the difficult n-dimensional constrained-optimization problem into a sequence of n easier scalar unconstrained problems that we solve efficiently via traditional wavelet shrinkage. Our method can handle arbitrary gradient-based regularizers. In particular, it can be made to adhere to the popular principle of least total variation. It can also be used as a maximum a posteriori estimator for a variety of priors. We illustrate the performance of our method for image denoising and for the statistical estimation of sparse stochastic processes.


@ARTICLE(http://bigwww.epfl.ch/publications/kamilov1201.html,
AUTHOR="Kamilov, U. and Bostan, E. and Unser, M.",
TITLE="Wavelet Shrinkage with Consistent Cycle Spinning Generalizes
        Total Variation Denoising",
JOURNAL="{IEEE} Signal Processing Letters",
YEAR="2012",
volume="19",
number="4",
pages="187--190",
month="April",
note="")

© 2012 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.