Deep Injective Prior for Inverse Scattering

TL;DR

This paper introduces a deep generative model-based framework for electromagnetic inverse scattering that learns a permittivity manifold, enabling robust reconstructions, uncertainty quantification, and applicability to real-world data without requiring paired training data.

Contribution

It presents a novel data-driven inverse scattering method using deep generative models and Bayesian inference, requiring only permittivity data for training, unlike supervised approaches.

Findings

Outperforms traditional iterative solvers on synthetic and experimental data.

Provides uncertainty estimates alongside permittivity reconstructions.

Achieves comparable results to state-of-the-art supervised methods like U-Net.

Abstract

In electromagnetic inverse scattering, the goal is to reconstruct object permittivity using scattered waves. While deep learning has shown promise as an alternative to iterative solvers, it is primarily used in supervised frameworks which are sensitive to distribution drift of the scattered fields, common in practice. Moreover, these methods typically provide a single estimate of the permittivity pattern, which may be inadequate or misleading due to noise and the ill-posedness of the problem. In this paper, we propose a data-driven framework for inverse scattering based on deep generative models. Our approach learns a low-dimensional manifold as a regularizer for recovering target permittivities. Unlike supervised methods that necessitate both scattered fields and target permittivities, our method only requires the target permittivities for training; it can then be used with any experimental setup. We also introduce a Bayesian framework for approximating the posterior distribution of the target permittivity, enabling multiple estimates and uncertainty quantification. Extensive experiments with synthetic and experimental data demonstrate that our framework outperforms traditional iterative solvers, particularly for strong scatterers, while achieving comparable reconstruction quality to state-of-the-art supervised learning methods like the U-Net.