SUNLayer: Stable denoising with generative networks

Deep neural networks, in particular generative adversarial networks by [Goodfellow et al., 2014] have been recently used to produce generative models for real world data that can capture very complex structures. This is especially true for natural images (see for instance [Nguyen et al., 2016]). Those generative priors have been successfully used to efficiently solve classical inverse problems in signal processing, like super resolution ([Johnson et al., 2016]) and compressed sensing ([Bora et al., 2017]). The latter numerically demonstrates that the generative prior can be exploited to solve the compressed sensing problem with ten times fewer measurements than the classic compressed sensing theory requires. Followup work by [Hand and Voroninski, 2017] recently explained the success of local methods (namely empirical risk minimization) in the compressed sensing task by assuming a generative model of a multi-layer neural network with random weights and ReLU activation functions. The aim of this paper is to propose a theoretical framework that will allow us to analyze neural networks in the context of another classical inverse problem in signal processing: signal denoising.