DAEs for Linear Inverse Problems: Improved Recovery with Provable Guarantees

TL;DR

This paper introduces a DAE-based method with provable guarantees for linear inverse problems, achieving faster, higher-quality reconstructions without hyperparameter tuning.

Contribution

It proposes a novel DAE-based approach with theoretical guarantees that significantly improves speed and quality in linear inverse problem recovery.

Findings

Speeds up recovery by over 100 times

Improves reconstruction quality by over 10 times

Eliminates the need for hyperparameter tuning

Abstract

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.