Computational Optimization and Applications

, Volume 54, Issue 2, pp 371–398

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

Authors

    • Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis GroupUniversity of Heidelberg
  • Florian Becker
    • Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis GroupUniversity of Heidelberg
  • Jan Lellmann
    • Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis GroupUniversity of Heidelberg
  • Stefania Petra
    • Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis GroupUniversity of Heidelberg
  • Christoph Schnörr
    • Heidelberg Collaboratory for Image Processing & Image and Pattern Analysis GroupUniversity of Heidelberg
Article

DOI: 10.1007/s10589-012-9456-0

Cite this article as:
Lenzen, F., Becker, F., Lellmann, J. et al. Comput Optim Appl (2013) 54: 371. doi:10.1007/s10589-012-9456-0

Abstract

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.

Keywords

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

Copyright information

© Springer Science+Business Media, LLC 2012