Journal of Mathematical Imaging and Vision

, Volume 59, Issue 3, pp 515–533 | Cite as

Optimal Selection of the Regularization Function in a Weighted Total Variation Model. Part II: Algorithm, Its Analysis and Numerical Tests

  • Michael Hintermüller
  • Carlos N. Rautenberg
  • Tao Wu
  • Andreas Langer


Based on the weighted total variation model and its analysis pursued in Hintermüller and Rautenberg 2016, in this paper a continuous, i.e., infinite dimensional, projected gradient algorithm and its convergence analysis are presented. The method computes a stationary point of a regularized bilevel optimization problem for simultaneously recovering the image as well as determining a spatially distributed regularization weight. Further, its numerical realization is discussed and results obtained for image denoising and deblurring as well as Fourier and wavelet inpainting are reported on.


Image restoration Weighted total variation regularization Spatially distributed regularization weight Fenchel predual Bilevel optimization Variance corridor Projected gradient method Convergence analysis 

Mathematics Subject Classification

94A08 68U10 49K20 49K30 49K40 49M37 65K15 


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsHumboldt-University of BerlinBerlinGermany
  2. 2.Department of MathematicsUniversity of StuttgartStuttgartGermany

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