  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 deep generative networks). 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 linear and nonlinear inverse
problems, and (b) empirically improves upon conventional techniques such as
back-propagation. We support our claims with the experimental results for
solving various inverse problems. 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 building
blocks towards a principled use of generative models in inverse problems with
more complete algorithmic understanding.
