Provably Convergent Algorithms for Solving Inverse Problems Using Generative Models

TL;DR

This paper introduces a theoretically grounded, convergent algorithm for inverse problems using deep generative models, demonstrating improved performance and robustness over traditional methods.

Contribution

It provides the first provably convergent algorithm for inverse problems with generative priors, including extensions for model mismatch scenarios.

Findings

Linear convergence guarantees for certain inverse problems

Empirical improvement over back-propagation techniques

Effective handling of model mismatch situations

Abstract

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.