Abstract
We introduce a new regularizer in the total variation family that promotes reconstructions with a given Lipschitz constant (which can also vary spatially). We prove regularizing properties of this functional and investigate its connections to total variation and infimal convolution type regularizers (Formula Presented) and, in particular, establish topological equivalence. Our numerical experiments show that the proposed regularizer can achieve similar performance as total generalized variation while having the advantage of a very intuitive interpretation of its free parameter, which is just a local estimate of the norm of the gradient. It also provides a natural approach to spatially adaptive regularization.
Original language | English |
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Title of host publication | Scale Space and Variational Methods in Computer Vision - 7th International Conference, SSVM 2019, Proceedings |
Editors | Jan Lellmann, Jan Modersitzki, Martin Burger |
Publisher | Springer Verlag |
Pages | 485-497 |
Number of pages | 13 |
ISBN (Print) | 9783030223670 |
DOIs | |
Publication status | Published - 5 Jun 2019 |
Event | 7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019 - Hofgeismar, Germany Duration: 30 Jun 2019 → 4 Jul 2019 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11603 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019 |
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Country/Territory | Germany |
City | Hofgeismar |
Period | 30/06/19 → 4/07/19 |
Bibliographical note
Funding Information:This work was supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777826 (NoMADS). MB acknowledges further support by ERC via Grant EU FP7 – ERC Consolidator Grant 615216 LifeInverse. YK acknowledges support of the Royal Society through a Newton International Fellowship. YK also acknowledges support of the Humbold Foundataion through a Humbold Fellowship he held at the University of Münster when this work was initiated. CBS acknowledges support from the Leverhulme Trust project on Breaking the non-convexity barrier, EPSRC grant Nr. EP/M00483X/1, the EPSRC Centre Nr. EP/N014588/1, the RISE projects CHiPS and NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute. We gratefully acknowledge the support of NVIDIA Corporation with the donation of a Quadro P6000 and a Titan Xp GPUs used for this research.
Funding Information:
Acknowledgments. This work was supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777826 (NoMADS). MB acknowledges further support by ERC via Grant EU FP7 – ERC Consolidator Grant 615216 LifeInverse. YK acknowledges support of the Royal Society through a Newton International Fellowship. YK also acknowledges support of the Humbold Foundataion through a Humbold Fellowship he held at the University of Münster when this work was initiated. CBS acknowledges support from the Leverhulme Trust project on Breaking the non-convexity barrier, EPSRC grant Nr. EP/M00483X/1, the EPSRC Centre Nr. EP/N014588/1, the RISE projects CHiPS and NoMADS, the Cantab Capital Institute for the Mathematics of Information and the Alan Turing Institute. We gratefully acknowledge the support of NVIDIA Corporation with the donation of a Quadro P6000 and a Titan Xp GPUs used for this research.
Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
Keywords
- First order regularization
- Image denoising
- Total generalized variation
- Total variation
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science