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. [SIAM J. Imaging Sci., 3 (2010)]. After studying the mathematical properties of DTGV, we utilize it as regularizer and propose the L 2 -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.
In REF , the continuous directional total variation (DTV) and directional total generalized variation (DTGV) are analysed for a single global direction θ:
Directional Total Generalized Variation Regularization
arXiv: Numerical Analysis
Mathematics