A Two-Stage Imaging Framework Combining CNN and Physics-Informed Neural Networks for Full-Inverse Tomography: A Case Study in Electrical Impedance Tomography (EIT)

2024-07-25

IEEE Signal Processing Letters

AI Summary

Electrical Impedance Tomography (EIT) is a severely ill-posed full inverse problem, where robust reconstruction of internal conductivity distributions from boundary voltage measurements alone remains highly challenging. To address key limitations of existing physics-informed neural networks (PINNs)—including reliance on unrealistic priors and poor generalizability—this paper proposes a two-stage CNN-PINN hybrid framework. In Stage I, a convolutional neural network (CNN) performs data-driven, coarse-grained reconstruction. In Stage II, the CNN’s output serves as an informed initial guess for a PINN explicitly constrained by the Laplace equation, enabling physics-consistent refinement. This work introduces the novel “data-driven initialization + model-driven optimization” paradigm, eliminating the need for idealized priors or calibrated training data while supporting mixed supervised/unsupervised learning. Experiments demonstrate substantial improvements in reconstruction accuracy, cross-dataset generalizability, and physical fidelity. The method provides a new, interpretable, robust, and assumption-free pathway for solving full inverse problems in EIT.

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• Constraint Satisfaction and Optimization: Satisfiability
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

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Abstract

Electrical Impedance Tomography (EIT) is a highly ill-posed inverse problem, with the challenge of reconstructing internal conductivities using only boundary voltage measurements. Although Physics-Informed Neural Networks (PINNs) have shown potential in solving inverse problems, existing approaches are limited in their applicability to EIT, as they often rely on impractical prior knowledge and assumptions that cannot be satisfied in real-world scenarios. To address these limitations, we propose a two-stage hybrid learning framework that combines Convolutional Neural Networks (CNNs) and PINNs. This framework integrates data-driven and model-driven paradigms, blending supervised and unsupervised learning to reconstruct conductivity distributions while ensuring adherence to the underlying physical laws, thereby overcoming the constraints of existing methods.

Problem

• Reconstruct internal conductivities from boundary voltage measurements.
• Overcome impractical prior knowledge in existing EIT methods.
• Combine CNNs and PINNs for accurate conductivity distribution reconstruction.

Innovation

• Two-stage hybrid learning framework for EIT
• Combines CNNs and Physics-Informed Neural Networks
• Integrates data-driven and model-driven paradigms