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BIT Numerical Mathematics

, Volume 59, Issue 4, pp 903–928 | Cite as

Directional total generalized variation regularization

  • Rasmus Dalgas Kongskov
  • Yiqiu DongEmail author
  • Kim Knudsen
Article
  • 140 Downloads

Abstract

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 \(\hbox {L}^2\hbox {-}\mathrm {DTGV}\) 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.

Keywords

Directional total generalized variation Prior information Regularization Variational model Primal-dual algorithm Image restoration 

Mathematics Subject Classification

49M29 65K10 65J22 90C47 94A08 

Notes

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Computer ScienceTechnical University of DenmarkKgs. LyngbyDenmark

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