Investigating the influence of box-constraints on the solution of a total variation model via an efficient primal-dual method
(2018) In Journal of Imaging 4(1).- 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... (More)
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 L 2 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.
(Less)
- author
- Langer, Andreas LU
- publishing date
- 2018
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Automated parameter selection, Box-constrained total variation minimization, Image reconstruction, Semi-smooth Newton
- in
- Journal of Imaging
- volume
- 4
- issue
- 1
- article number
- 12
- publisher
- MDPI AG
- external identifiers
-
- scopus:85063132692
- ISSN
- 2313-433X
- DOI
- 10.3390/jimaging4010012
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2018 by the author. Licensee MDPI, Basel, Switzerland. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.
- id
- 71e37f5c-1375-45af-afab-67419abf338b
- date added to LUP
- 2021-03-15 22:26:51
- date last changed
- 2022-04-19 05:17:31
@article{71e37f5c-1375-45af-afab-67419abf338b,
abstract = {{<p> 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 L <sup>2</sup> 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. </p>}},
author = {{Langer, Andreas}},
issn = {{2313-433X}},
keywords = {{Automated parameter selection; Box-constrained total variation minimization; Image reconstruction; Semi-smooth Newton}},
language = {{eng}},
number = {{1}},
publisher = {{MDPI AG}},
series = {{Journal of Imaging}},
title = {{Investigating the influence of box-constraints on the solution of a total variation model via an efficient primal-dual method}},
url = {{http://dx.doi.org/10.3390/jimaging4010012}},
doi = {{10.3390/jimaging4010012}},
volume = {{4}},
year = {{2018}},
}