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; R.D. Kongskov, Y. Dong K. Knudsen, BIT 59, 2019  in the case of impulse and Gaussian noise.
After 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 K. Knudsen, BIT 59, 2019 in the case of impulse and Gaussian noise.