A Total Variation Based Regularizer Promoting Piecewise-Lipschitz Reconstructions

Martin Burger, Yury Korolev, Carola Bibiane Schönlieb, Christiane Stollenwerk

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

1 Citation (SciVal)

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 languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision - 7th International Conference, SSVM 2019, Proceedings
EditorsJan Lellmann, Jan Modersitzki, Martin Burger
PublisherSpringer Verlag
Pages485-497
Number of pages13
ISBN (Print)9783030223670
DOIs
Publication statusPublished - 5 Jun 2019
Event7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019 - Hofgeismar, Germany
Duration: 30 Jun 20194 Jul 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11603 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019
Country/TerritoryGermany
CityHofgeismar
Period30/06/194/07/19

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

Fingerprint

Dive into the research topics of 'A Total Variation Based Regularizer Promoting Piecewise-Lipschitz Reconstructions'. Together they form a unique fingerprint.

Cite this