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

Author

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  • Frank Lenzen
  • Florian Becker
  • Jan Lellmann
  • Stefania Petra
  • Christoph Schnörr

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. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Frank Lenzen & Florian Becker & Jan Lellmann & Stefania Petra & Christoph Schnörr, 2013. "A class of quasi-variational inequalities for adaptive image denoising and decomposition," Computational Optimization and Applications, Springer, vol. 54(2), pages 371-398, March.
    • Handle: RePEc:spr:coopap:v:54:y:2013:i:2:p:371-398
    DOI: 10.1007/s10589-012-9456-0
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    References listed on IDEAS

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    1. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
    2. NESTEROV, Yu. & SCRIMALI, Laura, 2006. "Solving strongly monotone variational and quasi-variational inequalities," LIDAM Discussion Papers CORE 2006107, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Akhtar A. Khan & Dumitru Motreanu, 2018. "Inverse problems for quasi-variational inequalities," Journal of Global Optimization, Springer, vol. 70(2), pages 401-411, February.

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