A Model-Guided Neural Network Method for the Inverse Scattering Problem

TL;DR

This paper introduces a physics-informed neural network approach for inverse scattering problems, integrating a differentiable physics solver to improve reconstruction quality and efficiency in nonlinear wave-based imaging.

Contribution

It presents a novel model-guided neural network that explicitly incorporates the physics of scattering via a differentiable solver, enhancing accuracy and computational efficiency.

Findings

High-quality reconstructions achieved with reduced computational cost

Progressive refinement using increasing wave frequencies stabilizes recovery

Outperforms classical and other ML-based methods in accuracy and speed

Abstract

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in capturing prior knowledge of imaging targets relative to classical optimization-based approaches; however, they perform poorly in regimes where the scattering behavior is highly nonlinear. A key limitation is that ML methods struggle to incorporate the physics governing the scattering process, which are typically inferred implicitly from the training data or loosely enforced via architectural design. In this paper, we present a method that endows a machine learning framework with explicit knowledge of problem physics, in the form of a differentiable solver representing the forward model. The proposed method progressively refines reconstructions of the scattering potential using measurements at increasing wave frequencies, following a classical strategy to stabilize recovery. Empirically, we find that our method provides high-quality reconstructions at a fraction of the computational or sampling costs of competing approaches.