Learning Generative Models of Structured Signals from Their Superposition Using GANs with Application to Denoising and Demixing
This addresses the challenge of modeling distributions from mixed data in applications like signal processing, though it is incremental as it builds on existing GAN methods.
The paper tackles the problem of learning generative models from superimposed structured signals, where clean samples are not directly available, by proposing denoising-GAN and demixing-GAN frameworks. The result is that these frameworks can generate clean samples and achieve competitive performance in tasks like denoising, demixing, and compressive sensing, as demonstrated through numerical experiments.
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. However, in many applications, this assumption is violated. 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, demixing, and compressive sensing.