AGEM: Solving Linear Inverse Problems via Deep Priors and Sampling

In this paper we propose to use a denoising autoencoder (DAE) prior to simultaneously solve a linear inverse problem and estimate its noise parameter. Existing DAE-based methods estimate the noise parameter empirically or treat it as a tunable hyper-parameter. We instead propose autoencoder guided EM, a probabilistically sound framework that performs Bayesian inference with intractable deep priors. We show that efficient posterior sampling from the DAE can be achieved via Metropolis-Hastings, which allows the Monte Carlo EM algorithm to be used. We demonstrate competitive results for signal denoising, image deblurring and image devignetting.