Optimization for Amortized Inverse Problems

TL;DR

This paper introduces an amortized optimization method for inverse problems using deep generative priors, improving reconstruction quality by decomposing complex tasks into simpler ones, with theoretical guarantees and empirical validation.

Contribution

It proposes a novel amortized optimization scheme that better handles non-convex inverse problems with deep generative priors, outperforming existing methods.

Findings

Outperforms baseline methods qualitatively and quantitatively

Provides theoretical guarantees for the proposed algorithm

Validated on different inverse problems

Abstract

Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient descent largely without adapting to the non-convex nature of the problem and can be sensitive to initial values, impeding further performance improvement. In this paper, we propose an efficient amortized optimization scheme for inverse problems with a deep generative prior. Specifically, the optimization task with high degrees of difficulty is decomposed into optimizing a sequence of much easier ones. We provide a theoretical guarantee of the proposed algorithm and empirically validate it on different inverse problems. As a result, our approach outperforms baseline methods qualitatively and quantitatively by a large margin.