approach does not require hyperparameter tuning and is robust to the selection of the architecture of generator. In contrast to the conventional convolutional neural network, [**GAN**]{}s can generate clearer images. [**WGAN**]{}-$\ell_1$ proposed by Kupyn [*et al.*]{} [@kupyn2017deblurgan] has been shown effective in image deblurring.

[**TRN**]{}: Turbulence Removal Network
=======================================

In this section, we describe our proposed method based on deep convolutional neural network, namely, the [**T**]{}urbulence [**R**]{}emoval [**N**]{}etwork ([**TRN**]{}). Figure \[fig:net\] shows that whole network architecture for both the generator network $G$ and the critic network $D$.

Data Augmentation for Turbulence
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The first step of our proposed algorithm is to synthesize sufficient training data distorted by turbulence. A large sample size of training data is typically necessary for solving tasks using deep learning approaches, but unfortunately there is limited turbulence-distorted data available. This hinders the application of deep learning approaches for turbulence removal. To alleviate this issue, we introduce a new, simple but effective method for generating the training data from a few data for deep learning.

More specifically, a single (clean) frame $I$ is transformed to another image $I^t$ with geometric distortions and blurs as follows. We first select $Q = (w-2N) \times (w-2N)$ pixel positions randomly, where 