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

2025-12-10

AI Summary

To address poor generalizability and low stability in inverse scattering imaging caused by strong nonlinearity and ill-posedness, this paper proposes a physics-informed deep learning framework. Methodologically, it introduces, for the first time, an explicit, differentiable wave-equation solver deeply embedded into a neural network architecture, enabling a multi-frequency collaborative progressive reconstruction network and a physics-constrained end-to-end training scheme. By rigorously incorporating wave physics into forward modeling, the framework avoids black-box approximation and significantly enhances modeling fidelity for highly nonlinear scattering phenomena. Experimental results demonstrate superior imaging accuracy over state-of-the-art methods across medical imaging, remote sensing, and non-destructive testing tasks. Moreover, the framework reduces both computational cost and data requirements to less than 10% of those of competing approaches, achieving a favorable trade-off among high fidelity, strong generalizability, and computational efficiency.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Inverse medium scattering is ill-posed and nonlinear
• Machine learning methods struggle to incorporate explicit physics
• The method integrates a differentiable forward solver into ML

Innovation

• Integrates differentiable forward solver into neural network
• Uses multi-frequency measurements to stabilize reconstruction
• Combines physics-based modeling with machine learning efficiency