A Two-Stage Imaging Framework Combining CNN and Physics-Informed Neural Networks for Full-Inverse Tomography: A Case Study in Electrical Impedance Tomography (EIT)
Xuanxuan Yang, Yangming Zhang, Haofeng Chen, Gang Ma, Xiaojie Wang
TL;DR
This work tackles the ill-posed inverse problem of Electrical Impedance Tomography (EIT) by integrating a convolutional neural network (CNN) with a physics-informed neural network (PINN) in a two-stage framework. The CNN (an end-to-end U-Net) translates boundary voltage differences into an internal potential field, which the PINN then uses to infer the conductivity $\sigma(x,y)$ by enforcing the PDE $-$\nabla·$(\sigma ∇u)=0$ and boundary conditions, via a matrix-based finite-difference approach to compute derivatives. This hybrid method reduces computational cost by avoiding multiple networks for each excitation and enhances physical consistency through a PDE-constrained loss with regularization terms such as total variation. Experiments on synthetic data demonstrate robust reconstruction across complex geometries and indicate potential for real-time sensing and extension to other inverse imaging problems.
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.