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

M. Hintermüller, C.N. Rautenberg, T. Wu, A. Langer

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)515-533
Number of pages19
JournalJournal of Mathematical Imaging and Vision
Volume59
Early online date9 Jun 2017
DOIs
Publication statusE-pub ahead of print - 9 Jun 2017
Externally publishedYes

Keywords

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

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