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.

在压缩感知应用中，自学习生成模型引起了越来越多的关注，因为它们提供了与标准压缩感知类似的保证，而不采用稀疏性。然而，提高生成模型的性能是具有挑战性的。在本文中，我们通过利用相关域中原始信号向量支持的先验知识来提高生成模型（生成对抗网络）的恢复性能。我们展示了使用具有 Fisher 距离度量的参数模型在指定分布约束时利用支持上的分布的优势。我们将生成模型与Fisher距离结合起来研究满足分布的稀疏信号的恢复，目的是在分布有一些约束时提高模型的恢复性能。最后，我们展示了对模拟信号和成像信号进行的大量实验的结果。