On the Implicit Representation of the Electrical Impedance Tomography Inverse Problem

Electrical Impedance Tomography (EIT) is a noninvasive imaging method that reconstructs internal conductivity maps by applying low-frequency electrical currents through surface electrodes and measuring the resulting voltages. While EIT's inverse problem is inherently ill-posed, requiring regularization techniques to stabilize solutions, recent advances in neural networks offer promising alternatives for improving reconstruction accuracy. This study investigates the application of Deep Implicit Layers to EIT reconstruction, combining fixed-point iteration and Newton's method to solve implicit constraints. The forward problem is solved using the finite element method (FEM), and numerical phantoms are employed for training. To ensure a more realistic representation of measurement conditions, contact conductivity was modeled as a random variable sampled from a Gaussian distribution, improving the model's robustness and ability to handle uncertainties. The implicit neural network effectively distinguishes closely positioned objects; however, contrast limitations persist at the boundaries of the phantoms. The results highlight the potential of implicit models in EIT and suggest future improvements through advanced optimization techniques and expansion to 3D thorax reconstruction.