Cross-Scale Neural Representation for Electrical Impedance Tomography

Electrical Impedance Tomography is a non-invasive imaging modality that is radiation-free and cost-effective; yet, accurately estimating internal conductivity remains challenging due to its inherent ill-posedness and strong nonlinearity. Implicit Neural Representations have recently emerged as powerful unsupervised deep priors, enabling continuous parameterization of conductivity. However, the intuitively appealing strategy of solving forward problems on coarse discretizations for efficiency while querying on fine meshes for geometric details is affected by training-time discretization coupling. In existing methods, networks are queried only at coarse integration nodes during training, thereby coupling learning to the coarse discretization. This can lead to mesh-dependent distortions for continuous backbones and out-of-distribution degradation for topology-dependent backbones when transferred to finer meshes. To mitigate this issue, we propose Cross-Scale Neural Representation (CSNR), an unsupervised framework that explicitly decouples conductivity representation from forward-solver discretization within the training loop. CSNR integrates a Cross-Scale Regularization Network (CSR-Net) with L2 projection operators, enforcing fine-mesh representation under coarse-mesh physics while promoting cross-scale consistency and suppressing mesh-dependent distortions. Extensive simulated and experimental results demonstrate that CSNR achieves high reconstruction fidelity and mitigates backbone-specific failures across resolutions.