A Total Variation Based Regularizer Promoting Piecewise-Lipschitz Reconstructions

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

Research output: Chapter in 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

Keywords

  • First order regularization
  • Image denoising
  • Total generalized variation
  • Total variation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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