Directional total generalized variation regularization

Rasmus Dalgas Kongskov, Yiqiu Dong*, Kim Knudsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


In inverse problems, prior information and a priori-based regularization techniques play important roles. In this paper, we focus on image restoration problems, especially on restoring images whose texture mainly follow one direction. In order to incorporate the directional information, we propose a new directional total generalized variation (DTGV) functional, which is based on total generalized variation (TGV) by Bredies et al. After studying the mathematical properties of DTGV, we utilize it as regularizer and propose the L2-DTGV variational model for solving image restoration problems. Due to the requirement of the directional information in DTGV, we give a direction estimation algorithm, and then apply a primal-dual algorithm to solve the minimization problem. Experimental results show the effectiveness of the proposed method for restoring the directional images. In comparison with isotropic regularizers like total variation and TGV, the improvement of texture preservation and noise removal is significant.
Original languageEnglish
JournalBIT Numerical Mathematics
Number of pages26
Publication statusPublished - 2019


  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics
  • Directional total generalized variation
  • Image restoration
  • Primal-dual algorithm
  • Prior information
  • Regularization
  • Variational model

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