Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees
This work addresses the challenge of improving discriminative capability and providing theoretical guarantees in learning-based methods for linear inverse problems, which is important for researchers and practitioners in signal processing and machine learning, though it is incremental as it builds on existing GAN priors.
The paper tackles the problem of solving linear inverse problems like compressive sensing by replacing hand-crafted priors with a Generative Adversarial Network (GAN) prior, proposing a projected gradient descent algorithm with theoretical convergence guarantees and demonstrating superior empirical performance over existing GAN-based methods.
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.