Solving Inverse Problems with a Flow-based Noise Model

TL;DR

This paper introduces a novel approach for solving inverse image problems using a flow-based noise model, enabling the handling of complex noise dependencies and non-linear measurements, with empirical validation and initial theoretical guarantees.

Contribution

It presents a new formulation for inverse problems using flow-based priors that accommodates arbitrary noise dependencies and non-linear forward operators.

Findings

Effective in compressed sensing with quantized measurements

Successful in denoising with structured noise patterns

Provides initial theoretical recovery guarantees

Abstract

We study image inverse problems with a normalizing flow prior. Our formulation views the solution as the maximum a posteriori estimate of the image conditioned on the measurements. This formulation allows us to use noise models with arbitrary dependencies as well as non-linear forward operators. We empirically validate the efficacy of our method on various inverse problems, including compressed sensing with quantized measurements and denoising with highly structured noise patterns. We also present initial theoretical recovery guarantees for solving inverse problems with a flow prior.