Algorithmic Aspects of Inverse Problems Using Generative Models

TL;DR

This paper provides a theoretical analysis of using generative models like GANs for inverse problems, proposing algorithms with convergence guarantees and improved empirical performance over traditional methods.

Contribution

It introduces a simple non-convex algorithm with proven convergence for inverse problems using generative models and extends it to handle model mismatch scenarios.

Findings

Linear convergence guarantees for certain generative model-based inverse algorithms

Empirical improvements over back-propagation techniques

Extension to handle model mismatch scenarios

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 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 building blocks towards a more complete algorithmic understanding of generative models in inverse problems.