  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.
