Set-Valued and Variational Analysis

, Volume 18, Issue 3–4, pp 277–306 | Cite as

A Second-Order Model for Image Denoising

  • Maïtine BergouniouxEmail author
  • Loic Piffet


We present a variational model for image denoising and/or texture identification. Noise and textures may be modelled as oscillating components of images. The model involves a L 2-data fitting term and a Tychonov-like regularization term. We choose the BV 2 norm instead of the classical BV norm. Here BV 2 is the bounded hessian function space that we define and describe. The main improvement is that we do not observe staircasing effects any longer, during denoising process. Moreover, texture extraction can be performed with the same method. We give existence results and present a discretized problem. An algorithm close to the one set by Chambolle (J Math Imaging Vis 20:89–97, 2004) is used: we prove convergence and present numerical tests.


Second order total variation Image reconstruction Denoising Texture Variational method 

Mathematics Subject Classifications (2010)

65D18 68U10 65K10 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.UFR Sciences, Math., Labo. MAPMO, UMR 6628Université d’OrléansOrléans cedex 2France

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