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

In general the separation problem is inherently ill-posed; however, with enough structural assumption on X and N, it has been established that separation is possible. Depending on the application one might be interested in estimating only X (in this case, N is considered as the corruption), which is referred to as denoising, or in recovering both X and N which is referred to as demixing. Both demixing and denoising arise in a variety of important practical applications in the areas of signal/image processing, computer vision, machine learning, and statistics [Chen et al., 2001, Elad et al., 2005, Bobin et al., 2007, Candès et al., 2011]. Most of the existing techniques assume some prior knowledge on the structures of X and N in order to recover the desired component signal(s). Prior knowledge about the structure of X and N can only be obtained if one has access to the generative mechanism of the signals or has access to clean samples from the probability distribution defined over sets X and N . In many practical settings, neither of these may be feasible. In this paper, we consider the problem of separating constituent signals from superposed observations when clean access to samples from the distribution is not available.