Bilevel Image Denoising Using Gaussianity Tests

  • Jérôme Fehrenbach
  • Mila Nikolova
  • Gabriele Steidl
  • Pierre Weiss
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9087)


We propose a new methodology based on bilevel programming to remove additive white Gaussian noise from images. The lower-level problem consists of a parameterized variational model to denoise images. The parameters are optimized in order to minimize a specific cost function that measures the residual Gaussianity. This model is justified using a statistical analysis. We propose an original numerical method based on the Gauss-Newton algorithm to minimize the outer cost function. We finally perform a few experiments that show the well-foundedness of the approach. We observe a significant improvement compared to standard TV-\(\ell ^2\) algorithms and show that the method automatically adapts to the signal regularity.


Bilevel programming Image denoising Gaussianity tests Convex optimization 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jérôme Fehrenbach
    • 1
  • Mila Nikolova
    • 2
  • Gabriele Steidl
    • 3
  • Pierre Weiss
    • 4
  1. 1.CNRS, IMT (UMR5219) and ITAV (USR 3505)Université de ToulouseToulouseFrance
  2. 2.CNRS, CMLAENS CachanCachanFrance
  3. 3.University of KaiserslauternKaiserslauternGermany
  4. 4.CNRS, IMT (UMR5219) and ITAV (USR 3505)Université de ToulouseToulouseFrance

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