Investigating the influence of box-constraints on the solution of a total variation model via an efficient primal-dual method

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Abstract

In this paper, we investigate the usefulness of adding a box-constraint to the minimization of functionals consisting of a data-fidelity term and a total variation regularization term. In particular, we show that in certain applications an additional box-constraint does not effect the solution at all, i.e., the solution is the same whether a box-constraint is used or not. On the contrary, i.e., for applications where a box-constraint may have influence on the solution, we investigate how much it effects the quality of the restoration, especially when the regularization parameter, which weights the importance of the data term and the regularizer, is chosen suitable. In particular, for such applications, we consider the case of a squared L2 data-fidelity term. For computing a minimizer of the respective box-constrained optimization problems a primal-dual semi-smooth Newton method is presented, which guarantees superlinear convergence
Original languageEnglish
Article number70569
Number of pages34
JournalJournal of Imaging
Volume4
Issue number12
DOIs
Publication statusPublished - 6 Jan 2018
Externally publishedYes

Bibliographical note

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Keywords

  • box-constrained total variation minimization
  • semi-smooth Newton
  • image reconstruction
  • automated parameter selection

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