WIAS Preprint No. 2236, (2016)

Optimal selection of the regularization function in a generalized total variation model. Part II: Algorithm, its analysis and numerical tests


  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Rautenberg, Carlos N.
    ORCID: 0000-0001-9497-9296
  • Wu, Tao
  • Langer, Andreas

2010 Mathematics Subject Classification

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


  • Image restoration, generalized total variation regularization, spatially distributed regularization weight, Fenchel predual, bilevel optimization, variance corridor, pprojected gradient method, convergence analysis




Based on the generalized total variation model and its analysis pursued in part I (WIAS Preprint no. 2235), 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.

Appeared in

  • J. Math. Imaging Vision, 59 (2017), pp. 515--533.

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