Leaming Structured Signals Using GAN s with Applications in Denoising and Demixing

Recently, Generative Adversarial Networks (GANs) have emerged as a popular alternative for modeling complex high dimensional distributions. Most of the existing works implicitly assume that the clean samples from the target distribution are easily available, which is not true in real-world applications. In this paper, we consider the observation setting when the samples from target distribution are given by the superposition of two structured components and leverage GANs for learning the structure of the components. We propose two novel frameworks: denoising-GAN and demixing-GAN. The denoising-GAN assumes access to clean samples from the second component and try to learn the other distribution, whereas demixing-GAN learns the distribution of the components at the same time. Through extensive numerical experiments, we demonstrate that proposed frameworks can generate clean samples from unknown distributions, and provide competitive performance in tasks such as denoising and demixing.