Optimization for Amortized Inverse Problems
This work addresses a bottleneck in image reconstruction for inverse problems, offering an incremental improvement in optimization efficiency and robustness.
The paper tackles the challenge of using deep generative models as priors in inverse problems, where existing gradient descent methods are sensitive to initial values and non-convexity, by proposing an amortized optimization scheme that decomposes the task into easier subproblems, resulting in significant qualitative and quantitative improvements over baselines.
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.