approach is the joint subsampling and reconstruction variational model proposed by Lau [*et al.*]{} [@lau2017variational]. An advantage of the model is that there is no registration involved during the subsampling and reconstruction processes, and hence it is computationally efficient. Using the proposed energy model with various fidelity terms, restoration of turbulence-distorted images of different degrees of distortions can be achieved.

Generative Adversarial Networks
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Generative adversarial networks ([**GAN**]{}s) firstly proposed by Goodfellow at al. [@goodfellow2014generative] defines two separated competitors: the generator $G_{\theta}$ and the discriminator $D_{\xi} $. The generator is designed to produce samples from noise $\mathcal{Z}$ while a discriminator is designed to distinguish real sample $y_i$ and generated sample $G_\theta(z_i)$. The main objective of the generator is to generate perceptually persuasive samples that are challenging to be discriminated by the real samples. The competition between the generator $G$ and the discriminator $D$ can be described by the minimax objective shown as follows: $$\underset{G}{\min}  \underset{D}{\max} \quad \underset{x  \sim \mathbb{P}_r} { \mathbb{E} } [\log D(x)] + \underset{\tilde{x}  \sim \mathbb{P}_g} { \mathbb{E} } [\log (1-D(\tilde{x}))]$$ where $ \mathbb{P}_r $ is the data distribution and $\mathbb{P}_g$ is the generated distribution given by $\tilde{x}  = G(z), z \sim P(z)$, where $z$ is sampled from 