Algorithmic Aspects of Inverse Problems Using Generative Models

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by generative adversarial networks, or GANs). In this work, we study the algorithmic aspects of such a learning-based approach from a theoretical perspective. For certain generative network architectures, we establish a simple non-convex algorithmic approach that (a) theoretically enjoys linear convergence guarantees for certain inverse problems, and (b) empirically improves upon conventional techniques such as back-propagation. We also propose an extension of our approach that can handle model mismatch (i.e., situations where the generative network prior is not exactly applicable.) Together, our contributions serve as further building blocks towards an algorithmic theory of generative models in inverse problems.