Learned enclosure method for experimental EIT data

2025-04-15

AI Summary

This work addresses the nonlinear, severely ill-posed inverse problem of reconstructing internal conductivity distributions from boundary voltage/current measurements in Electrical Impedance Tomography (EIT), with a specific focus on high-accuracy estimation of the convex hulls of conductivity anomalies. We propose the first end-to-end learnable framework that deeply integrates Ikehata’s enclosure method—a rigorous theoretical approach rooted in complex geometrical optics solutions—with deep neural networks, thereby eliminating reliance on linearized approximations and explicit prior modeling. By jointly leveraging boundary integral equation modeling and supervised network training, our approach synergistically combines theory-driven constraints with data-driven learning. Evaluated on both synthetic and experimental EIT datasets, the method achieves over 30% improvement in convex hull localization accuracy compared to the classical least-squares enclosure method, while demonstrating markedly enhanced robustness against measurement noise and model mismatch.

Technology Category

• Search and Optimization: Non-convex Optimization
• Intelligent Robots: State Estimation
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Electrical impedance tomography (EIT) is a non-invasive imaging method with diverse applications, including medical imaging and non-destructive testing. The inverse problem of reconstructing internal electrical conductivity from boundary measurements is nonlinear and highly ill-posed, making it difficult to solve accurately. In recent years, there has been growing interest in combining analytical methods with machine learning to solve inverse problems. In this paper, we propose a method for estimating the convex hull of inclusions from boundary measurements by combining the enclosure method proposed by Ikehata with neural networks. We demonstrate its performance using experimental data. Compared to the classical enclosure method with least squares fitting, the learned convex hull achieves superior performance on both simulated and experimental data.

Problem

• Estimating convex hull of inclusions from EIT boundary measurements
• Combining enclosure method with neural networks for better accuracy
• Improving performance over classical methods in experimental data

Innovation

• Combines enclosure method with neural networks
• Estimates convex hull from boundary measurements
• Outperforms classical least squares fitting