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


Authors

  • 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

Keywords

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

DOI

10.20347/WIAS.PREPRINT.2236

Abstract

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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