the $\ell_1$ or $\ell_2$ error, is insufficient to produce a clear image [@ledig2017photo]. Besides, the $\ell_2$ error term can often cause image blur. Thus, we employ $\ell_1$ error, instead of the $\ell_2$ error, in our loss function $L_G$ to make the image much less blurry. Experimental results demonstrate that the combination of the two terms in the loss function $L_G$ can effectively remove geometric distortions and undesirable artifacts, such as image blurs.

### Critic Network

The critic network $D$ in the [**WGAN**]{} [@arjovsky2017wasserstein] is a deep [**CNN**]{} involving convolutional layers, fully-connected layer, ReLU activation layer [@nair2010rectified] and instance normalization layer [@ulyanovinstance]. We denote the first 6 convolutional layers by $L^{(1)}, L^{(2)},...,L^{(6)}$ and the last fully connected layer by $L^{(7)}$. The critic values $D \circ G(I_{TD}))$ and $D \circ I_C$ are passed into the critic network to output the Wasserstain-1 distance $$\underset{ {\Vert D \Vert}_L \leq 1}{\max}  \quad \underset{x  \sim \mathbb{P}_r} { \mathbb{E} } [ D(x)] - \underset{\tilde{x}  \sim \mathbb{P}_g} { \mathbb{E} } [ D(\tilde{x})]$$ The critic network $D$ is trained till optimal before updating the generator network $G$. The loss function of the critic network $D$ in the training process is provided as follows: $$L_D = D(G(I_{TD})) - D(G(I_C)) + 