Compressed sensing using generative models based on fisher information

In compressed sensing applications, self-learning generative models have attracted increasing attention because they provide guarantees that are similar to those of standard compressed sensing without employing sparsity. However, improving the performances of a generative model is challenging. In this paper, we improve the recovery performances of generative models (generative adversarial networks) by making use of prior knowledge about the support of the vector of the original signal in the relevant domain. We demonstrate the advantage of using a parametric model with the Fisher distance metric for the exploitation of a distribution over the support when constraints on the distribution have been specified. We combine the generative model with the Fisher distance to study the recovery of sparse signals that satisfy a distribution for the purpose of improving the recovery performance of the model when there are some constraints on the distribution. Finally, we present the results of extensive experiments conducted on simulated signals and imaging signals.