Compressed Sensing with Invertible Generative Models and Dependent Noise

Jay Whang, Qi Lei, Alex Dimakis

Keywords: invertible generative model, inverse problem, compressed sensing, normalizing flow

TL;DR: A method to solve inverse problems with structured noise and non-linear forward operator using a normalizing flow prior.

Abstract: We study image inverse problems with invertible generative priors, specifically normalizing flow models. Our formulation views the solution as the maximum a posteriori (MAP) estimate of the image given the measurements. Our general formulation allows for any differentiable noise model with long-range dependencies as well as non-linear differentiable forward operators. We establish theoretical recovery guarantees for denoising and compressed sensing under our framework. We also empirically validate our method on various inverse problems including 1-bit compressed sensing and denoising with highly structured noise patterns.