Adaptive Second-Order Total Variation: An Approach Aware of Slope Discontinuities

  • Frank Lenzen
  • Florian Becker
  • Jan Lellmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7893)


Total variation (TV) regularization, originally introduced by Rudin, Osher and Fatemi in the context of image denoising, has become widely used in the field of inverse problems. Two major directions of modifications of the original approach were proposed later on. The first concerns adaptive variants of TV regularization, the second focuses on higher-order TV models. In the present paper, we combine the ideas of both directions by proposing adaptive second-order TV models, including one anisotropic model. Experiments demonstrate that introducing adaptivity results in an improvement of the reconstruction error.


second-order total variation adaptive anisotropic directional TV TGV slope discontinuities 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Frank Lenzen
    • 1
  • Florian Becker
    • 1
  • Jan Lellmann
    • 2
  1. 1.Heidelberg Collaboratory for Image Processing (HCI)HeidelbergGermany
  2. 2.DAMTPUniversity of CambridgeUK

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