Computational Optimization and Applications

, Volume 54, Issue 2, pp 371–398 | Cite as

A class of quasi-variational inequalities for adaptive image denoising and decomposition

  • Frank LenzenEmail author
  • Florian Becker
  • Jan Lellmann
  • Stefania Petra
  • Christoph Schnörr


We introduce a class of adaptive non-smooth convex variational problems for image denoising in terms of a common data fitting term and a support functional as regularizer. Adaptivity is modeled by a set-valued mapping with closed, compact and convex values, that defines and steers the regularizer depending on the variational solution. This extension gives rise to a class of quasi-variational inequalities. We provide sufficient conditions for the existence of fixed points as solutions, and an algorithm based on solving a sequence of variational problems. Denoising experiments with spatial and spatio-temporal image data and an adaptive total variation regularizer illustrate our approach.


Quasi-variational inequalities Adaptive image denoising Total variation regularization Solution-dependent adaptivity 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Frank Lenzen
    • 1
    Email author
  • Florian Becker
    • 1
  • Jan Lellmann
    • 1
  • Stefania Petra
    • 1
  • Christoph Schnörr
    • 1
  1. 1.Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis GroupUniversity of HeidelbergHeidelbergGermany

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