Deep Variational Inverse Scattering

TL;DR

This paper introduces U-Flow, a Bayesian U-Net model that improves uncertainty quantification in inverse scattering problems by generating high-quality posterior samples, outperforming existing normalizing flow methods.

Contribution

The paper presents U-Flow, a novel Bayesian U-Net architecture that enhances posterior sampling quality and uncertainty estimation in inverse medium scattering.

Findings

U-Flow produces higher-quality posterior samples than recent normalizing flows.

U-Flow maintains comparable point estimation performance to standard U-Nets.

The method provides physically meaningful uncertainty estimates.

Abstract

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and noise can make this single estimate inaccurate or misleading. While deep networks such as conditional normalizing flows can be used to sample posteriors in inverse problems, they often yield low-quality samples and uncertainty estimates. In this paper, we propose U-Flow, a Bayesian U-Net based on conditional normalizing flows, which generates high-quality posterior samples and estimates physically-meaningful uncertainty. We show that the proposed model significantly outperforms the recent normalizing flows in terms of posterior sample quality while having comparable performance with the U-Net in point estimation.