We present a method to restore a clear image from a haze-affected image using a Wasserstein generative adversarial network. As the problem is ill-conditioned, previous methods have required a prior on natural images or multiple images of the same scene. We train a generative adversarial network to learn the probability distribution of clear images conditioned on the haze-affected images using the Wasserstein loss function, using a gradient penalty to enforce the Lipschitz constraint. The method is data-adaptive, end-to-end, and requires no further processing or tuning of parameters. We also incorporate the use of a texture-based loss metric and the L1 loss to improve results, and show that our results are better than the current state-of-the-art.
@math describes the 1-Lipschitz family of functions. In this formulation, @math is no longer called the discriminator, but is called the critic. This is because it does not perform classification, but simply produces a score that goes towards forming the objective function that is to be maximized with respect to @math and minimized with respect to @math . proposed to clip the weights of the critic in order to enforce the 1-Lipschitz constraint, which biases the critic towards simpler functions and requires careful tuning of the clipping parameter. Instead, @cite_6 proposed an alternative way to enforce the Lipschitz constraint, based on the observation that a function is 1-Lipschitz if and only if it has gradients of norm at most 1 everywhere. The new conditional WGAN objective then becomes:
@cite_6
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Generative Adversarial Networks (GANs) are powerful generative models, but suffer from training instability. The recently proposed Wasserstein GAN (WGAN) makes progress toward stable training of GANs, but sometimes can still generate only poor samples or fail to converge. We find that these problems are often due to the use of weight clipping in WGAN to enforce a Lipschitz constraint on the critic, which can lead to undesired behavior. We propose an alternative to clipping weights: penalize the norm of gradient of the critic with respect to its input. Our proposed method performs better than standard WGAN and enables stable training of a wide variety of GAN architectures with almost no hyperparameter tuning, including 101-layer ResNets and language models with continuous generators. We also achieve high quality generations on CIFAR-10 and LSUN bedrooms.