kernel $w(n) = \exp(-\frac{n^2}{2 B^2})$. The parameter $B$ is sampled uniformly from $[0.1,1]$. The final transformed image with geometric distortions and blurs is given by $I^i = w*I^t$. Using the proposed algorithm with randomized parameters, an original clean image $I^C$ is transformed into a sequence of images $\{I_1,...,I_n\}$ with geometric distortions and blurs for training. Figure \[fig:distortion\_strength\] shows some of the transformed images with different strength values. Experimental results suggest that this proposed algorithm with random parameters can successfully cover most possible deformations and hence geometric distortions can be successfully learnt from the deep network.

The data augmentation algorithm to synthesize turbulence-distorted video frames for training is summarized in Algorithm \[alg:distortion\_blur\_generation\]. Figure \[fig:augmentation\] illustrates the overall procedure of the data augmentation algorithm.

![image](augmentation.png)

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   ![image](augment_S1.png)   ![image](augment_S2.png)   ![image](augment_S3.png)   ![image](augment_S4.png)
             (a)                        (b)                        (c)                        (d)
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[**WGAN**]{}$-\ell_1$ with Multiframe Input
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The proposed turbulence removal network ([**TRN**]{}) is a multi-frame subsampled [**WGAN**]{} with the $\ell_1$ cost incorporated into the model. Multiframe input is adopted in [**TRN**]{} to absorb sufficient information on the turbulence deformation of the original image. Then, [**TRN**]{} is trained to remove geometric distortions and blurs with the [**WGAN**]{} architecture. The additional $\ell_1$ cost attempts 