2017/01/10 by Rasmus Dalgas Kongskov, Yiqiu Dong, Kongskov, Rasmus Dalgas +3 · 2 citations
Engineering · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1701.02675
openalex publication_date 2017/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 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.