Algorithmic Aspects of Inverse Problems Using Generative Models
This work addresses algorithmic challenges in inverse problems for researchers in computational imaging or signal processing, though it appears incremental as building blocks toward a more complete understanding.
The authors tackled the problem of solving inverse problems using generative models as learned priors instead of hand-crafted ones, establishing a non-convex algorithmic approach with theoretical linear convergence guarantees and empirical improvements over conventional techniques like back-propagation.
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.