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• W1782294490 abstract "Using first principles, we establish in this paper a connection between the maximum 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 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." @default.
• W1782294490 created "2016-06-24" @default.
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• W1782294490 date "2001-01-01" @default.
• W1782294490 modified "2023-09-27" @default.
• W1782294490 title "A Variational Approach to Maximum a Posteriori Estimation for Image Denoising" @default.
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• W1782294490 doi "https://doi.org/10.1007/3-540-44745-8_2" @default.
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