In recent works, both sparsity-based methods as well as learning-based
methods have proven to be successful in solving several challenging linear
inverse problems. However, sparsity priors for natural signals and images
suffer from poor discriminative capability, while learning-based methods seldom
provide concrete theoretical guarantees. In this work, we advocate the idea of
replacing hand-crafted priors, such as sparsity, with a Generative Adversarial
Network (GAN) to solve linear inverse problems such as compressive sensing. In
particular, we propose a projected gradient descent (PGD) algorithm for
effective use of GAN priors for linear inverse problems, and also provide
theoretical guarantees on the rate of convergence of this algorithm. Moreover,
we show empirically that our algorithm demonstrates superior performance over
an existing method of leveraging GANs for compressive sensing.

本研究使用生成对抗网络（GAN）代替稀疏性等手工先验知识来解决线性反问题，提出了一种有效的 PGD 算法，并提供了理论保证，该算法展现出优于现有方法的性能。