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Recently, Generative Adversarial Networks (GANs) have emerged as a popularalternative for modeling complex high dimensional distributions. Most of theexisting works implicitly assume that the clean samples from the targetdistribution are easily available. However, in many applications, thisassumption is violated. In this paper, we consider the observation setting whenthe samples from target distribution are given by the superposition of twostructured components and leverage GANs for learning the structure of thecomponents. We propose two novel frameworks: denoising-GAN and demixing-GAN.The denoising-GAN assumes access to clean samples from the second component andtry to learn the other distribution, whereas demixing-GAN learns thedistribution of the components at the same time. Through extensive numericalexperiments, we demonstrate that proposed frameworks can generate clean samplesfrom unknown distributions, and provide competitive performance in tasks suchas denoising, demixing, and compressive sensing.

Learning Generative Models of Structured Signals from Their Superposition Using GANs with Application to Denoising and Demixing