  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.
