original undistorted image.

The generator network is not pre-trained, since the input of the architecture is different from the conventional one. The conventional model takes the three channels of the image as input. In our case, we have a subsample of turbulence-distorted video frames $\mathcal{J}$, which are randomly chosen in the training stage and selected by the subsampling method introduced in the last subsection in the testing stage. The generator network $G$ is trained after the critic network $D$ is trained multiple times to give a clearer image $I_{TD} = G(I_{TD}^{(i_1)},...,I_{TD}^{(i_m)})$. The loss function of the generator network for removing geometric distortion and blurs is defined by $$L_G = - \sum_{n=1}^N  D(I_{TD}) +  \dfrac{\gamma}{N} {\Vert I_C - I_{TD} \Vert}_1$$ The first term in the loss function $L_G$ is the adversarial loss that encourages solutions to reside on the manifold of natural images. In order to retain the textures inherited from the turbulence-distorted video frames, we further incorporate the $\ell_1$ loss into the loss function $L_G$. Note that the combination of the pixel-wise error term with the adversarial loss has an advantage. It was suggested that the minimization of the loss function that contains only the pixel-wise error term, such as 