Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1001.68630
Ben Hamza, A.; Krim, Hamid
A variational approach to maximum {\it a posteriori} estimation for image denoising. (English)
[A] Figueiredo, Mário (ed.) et al., Energy minimization methods in computer vision and pattern recognition. 3rd international workshop, EMMCVPR 2001, Sophia Antipolis, France, September 3-5, 2001. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 2134, 19-33 (2001). ISBN 3-540-42523-3

Summary: Using first principles, we establish in this paper a connection between the maximum {\it a posteriori} (MAP) estimator and the variational formulation of optimizing a given functional subject to some noise constraints. A MAP estimator which uses a Markov or a maximum entropy random field model for a prior distribution can be viewed as a minimizer of a variational problem. Using notions from robust statistics, a variational filter called {\it Huber gradient descent flow} is proposed. It yields the solution to a Huber type functional subject to some noise constraints, and the resulting filter behaves like a total variation anisotropic diffusion for large gradient magnitudes and like an isotropic diffusion for small gradient magnitudes. Using some of the gained insight, we are also able to propose an information-theoretic gradient descent flow whose functional turns out to be a compromise between a neg-entropy variational integral and a total variation. Illustrating examples demonstrate a much improved performance of the proposed filters in the presence of Gaussian and heavy tailed noise.

MSC 2000:: *68U99 Computing methodologies
68T10 Pattern recognition
68T45 Machine vision and scene understanding

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]