Investigating the Influence of Box-Constraints on the Solution of a Total Variation Model via an Efficient Primal-Dual Method
Department of Mathematics, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
J. Imaging 2018, 4(1), 12; https://doi.org/10.3390/jimaging4010012
Received: 2 October 2017
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Revised: 2 January 2018
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Accepted: 3 January 2018
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Published: 6 January 2018
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 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.
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Keywords:
box-constrained total variation minimization; semi-smooth Newton; image reconstruction; automated parameter selection
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MDPI and ACS Style
Langer, A. Investigating the Influence of Box-Constraints on the Solution of a Total Variation Model via an Efficient Primal-Dual Method. J. Imaging 2018, 4, 12. https://doi.org/10.3390/jimaging4010012
AMA Style
Langer A. Investigating the Influence of Box-Constraints on the Solution of a Total Variation Model via an Efficient Primal-Dual Method. Journal of Imaging. 2018; 4(1):12. https://doi.org/10.3390/jimaging4010012
Chicago/Turabian StyleLanger, Andreas. 2018. "Investigating the Influence of Box-Constraints on the Solution of a Total Variation Model via an Efficient Primal-Dual Method" Journal of Imaging 4, no. 1: 12. https://doi.org/10.3390/jimaging4010012
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