DAEs for Linear Inverse Problems: Improved Recovery with Provable Guarantees
This work addresses efficiency and quality problems in compressive sensing, inpainting, and super-resolution for researchers and practitioners, though it is incremental as it builds on existing generative prior methods.
The paper tackles the slow speed, deficient reconstruction quality, and hyperparameter tuning issues in generative priors for linear inverse problems by using Denoising Auto Encoders (DAEs) and a projected gradient descent algorithm, resulting in over 100x faster recovery, over 10x improved reconstruction quality, and no hyperparameter tuning.
Generative priors have been shown to provide improved results over sparsity priors in linear inverse problems. However, current state of the art methods suffer from one or more of the following drawbacks: (a) speed of recovery is slow; (b) reconstruction quality is deficient; (c) reconstruction quality is contingent on a computationally expensive process of tuning hyperparameters. In this work, we address these issues by utilizing Denoising Auto Encoders (DAEs) as priors and a projected gradient descent algorithm for recovering the original signal. We provide rigorous theoretical guarantees for our method and experimentally demonstrate its superiority over existing state of the art methods in compressive sensing, inpainting, and super-resolution. We find that our algorithm speeds up recovery by two orders of magnitude (over 100x), improves quality of reconstruction by an order of magnitude (over 10x), and does not require tuning hyperparameters.