[@lau2017variational] to select the most useful frames as the input. The incorporating of the subsampling method into the network is shown to be effective in obtaining a significantly better restored image.

We now describe the subsampling method we incorporate in the network in details. Given a turbulence-distorted video frames $ \mathcal{I}_{TD} = (I_{TD}^{(1)}, I_{TD}^{(2)}, ..., I_{TD}^{(n)}) $, we consider a variational model to get an optimal subsample set $\mathcal{J}$ of sharp and mildly distorted images. $J = \{ i_1, \cdots, i_m \}$ is the index set of the subsample set $\mathcal{J}$, where $m = \vert J \vert$ is the number of chosen video frames in the subsample. Simultaneously, we obtain a reference image $I_R$ from the subsample set $J$. The variational model is formulated in the following form: $$\label{eq: energy}
E(I_R,J) = \dfrac{1}{\vert J \vert} \bigg(\sum_{k \in J}\mathcal{F}( I_R, I_{TD}^{(k)}) + \lambda \mathcal{Q} (I_{TD}^{(k)}) \bigg)  - {\tau} \mathcal{R}(J)$$ The fidelity term $\mathcal{F}$ is the discrepancy term between the reference image and the video frames. In our model, we define $\mathcal{F}( I_R, I_{TD}^{(k)}) = {\Big\Vert I_R - I_{TD}^{(k)} \Big\Vert}_2^2 $ for measuring the $\ell_2$ distance between the reference image $I_R$ and the subsampled video $\{I_{TD}^{(k)}\}_{k \in J}$. The quality term $\mathcal{Q}(I_{TD}^{(k)})$ 