Filters

20162

More filters

20192
Reset filters

Settings

DDC: 510 × Subject: variance corridor ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Optimal selection of the regularization function in a generalized total variation model. Part II: Algorithm, its analysis and numerical tests
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Hintermüller, Michael; Rautenberg, Carlos N.; Wu, Tao; Langer, Andreas
    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.
  • Thumbnail Image
    Item
    Optimal selection of the regularization function in a generalized total variation model. Part I: Modelling and theory
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Hintermüller, Michael; Rautenberg, Carlos N.
    A generalized total variation model with a spatially varying regularization weight is considered. Existence of a solution is shown, and the associated Fenchel-predual problem is derived. For automatically selecting the regularization function, a bilevel optimization framework is proposed. In this context, the lower-level problem, which is parameterized by the regularization weight, is the Fenchel predual of the generalized total variation model and the upper-level objective penalizes violations of a variance corridor. The latter object relies on a localization of the image residual as well as on lower and upper bounds inspired by the statistics of the extremes.