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This article is part of the series Nonlinear Signal and Image Processing - Part II.

Open Access Research Article

A Nonlinear Entropic Variational Model for Image Filtering

A Ben Hamza1*, Hamid Krim2 and Josiane Zerubia3

Author Affiliations

1 Concordia Institute for Information Systems Engineering, Concordia University, Montréal, Quebec H3G 1T7, Canada

2 Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695-7911, USA

3 Ariana Research Group, INRIA/I3S, BP 93, Sophia Antipolis Cedex, 06902, France

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EURASIP Journal on Advances in Signal Processing 2004, 2004:540425  doi:10.1155/S1110865704407197

The electronic version of this article is the complete one and can be found online at: http://asp.eurasipjournals.com/content/2004/16/540425


Received:12 August 2003
Revisions received:8 June 2004
Published:2 December 2004

© 2004 Ben Hamza et al.

We propose an information-theoretic variational filter for image denoising. It is a result of minimizing a functional subject to some noise constraints, and takes a hybrid form of a negentropy variational integral for small gradient magnitudes and a total variational integral for large gradient magnitudes. The core idea behind this approach is to use geometric insight in helping to construct regularizing functionals and avoiding a subjective choice of a prior in maximum a posteriori estimation. Illustrative experimental results demonstrate a much improved performance of the approach in the presence of Gaussian and heavy-tailed noise.

Keywords:
MAP estimation; variational methods; robust statistics; differential entropy; gradient descent flows; image denoising

Research Article