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


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

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding

F. Luisier, T. Blu, M. Unser

IEEE Transactions on Image Processing, vol. 16, no. 3, pp. 593-606, March 2007.



This paper introduces a new approach to orthonormal wavelet image denoising. Instead of postulating a statistical model for the wavelet coefficients, we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights. We then minimize an estimate of the mean square error between the clean image and the denoised one. The key point is that we have at our disposal a very accurate, statistically unbiased, MSE estimate—Stein's unbiased risk estimate—that depends on the noisy image alone, not on the clean one. Like the MSE, this estimate is quadratic in the unknown weights, and its minimization amounts to solving a linear system of equations. The existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients. Instead, and contrary to the custom in the literature, these coefficients are not considered random anymore. We describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near-optimal performance—both regarding quality and CPU requirement—by comparing with the results of three state-of-the-art nonredundant denoising algorithms on a large set of test images. An interesting fallout of this study is the development of a new, group-delay-based, parent-child prediction in a wavelet dyadic tree.

IEEE Signal Processing Society's 2009 Young Author Best Paper Award


@ARTICLE(http://bigwww.epfl.ch/publications/luisier0701.html,
AUTHOR="Luisier, F. and Blu, T. and Unser, M.",
TITLE="A New {SURE} Approach to Image Denoising: {I}nterscale
        Orthonormal Wavelet Thresholding",
JOURNAL="{IEEE} Transactions on Image Processing",
YEAR="2007",
volume="16",
number="3",
pages="593--606",
month="March",
note="{IEEE Signal Processing Society's 2006 young author best paper
        award}")

© 2007 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.