Before revision:  In order to deal with these problems, the Directional Total Generalized Variation (DTGV) has been presented in R.D. Kongskov Y. Dong, SSVM 2017 , LNCS 10302, 2017;
After revision:  In order to deal with these problems, the Directional Total Generalized Variation (DTGV) has been presented in  Y. Dong, SSVM 2017 , LNCS 10302, 2017;