An Improved Mesh-Free Approach for Electrical Impedance Tomography Using Modified Element-Free Galerkin Method and Neural Network Correction

Electrical Impedance Tomography (EIT) is a promising imaging modality whose accuracy strongly depends on the precision of its forward problem solution. In this study, a Modified Element-Free Galerkin Method (MEFG) is developed to solve both forward and inverse problems in EIT. The MEFG approach preserves the mesh-free advantages of the conventional Element-Free Galerkin (EFG) Method while directly imposing essential boundary conditions through modified shape functions that satisfy the Kronecker delta property. To further improve reconstruction accuracy, a back-propagation neural network is trained to reduce discrepancies between simulated and exact data during inverse problem. Numerical experiments using a heterogeneous model demonstrate that MEFG achieves superior forward model accuracy compared to the traditional finite element method. Additionally, the MEFG improves image reconstruction stability in the presence of measurement noise, validating the robustness of the proposed approach for practical biomedical EIT applications.