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A Nonlinear Entropic Variational Model for Image Filtering

Abstract

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.

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Correspondence to A. Ben Hamza.

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Ben Hamza, A., Krim, H. & Zerubia, J. A Nonlinear Entropic Variational Model for Image Filtering. EURASIP J. Adv. Signal Process. 2004, 540425 (2004). https://doi.org/10.1155/S1110865704407197

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Keywords and phrases

  • MAP estimation
  • variational methods
  • robust statistics
  • differential entropy
  • gradient descent flows
  • image denoising
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