Physics-Driven Neural Compensation For Electrical Impedance Tomography

TL;DR

Electrical Impedance Tomography (EIT) faces ill-posed inverse problems and spatially varying sensitivity that limit reconstruction quality. PhyNC introduces a physics-driven neural compensation framework that couples a neural field with the EIT forward model and uses sensitivity-based level mapping plus a hybrid Mip-Map and Fourier-embedding representation to allocate capacity where the forward model is weak. A frequency-regularized unsupervised objective enforces consistency with boundary voltages produced by the forward operator, enabling high-detail reconstructions and artifact resistance without ground-truth data. Extensive experiments on both simulated and experimental data show that PhyNC outperforms traditional regularization and prior neural-field approaches, especially in low-sensitivity regions and on coarser meshes, demonstrating robust, practical gains for EIT and potential applicability to other imaging modalities with similar challenges.

Abstract

Electrical Impedance Tomography (EIT) provides a non-invasive, portable imaging modality with significant potential in medical and industrial applications. Despite its advantages, EIT encounters two primary challenges: the ill-posed nature of its inverse problem and the spatially variable, location-dependent sensitivity distribution. Traditional model-based methods mitigate ill-posedness through regularization but overlook sensitivity variability, while supervised deep learning approaches require extensive training data and lack generalization. Recent developments in neural fields have introduced implicit regularization techniques for image reconstruction, but these methods typically neglect the physical principles underlying EIT, thus limiting their effectiveness. In this study, we propose PhyNC (Physics-driven Neural Compensation), an unsupervised deep learning framework that incorporates the physical principles of EIT. PhyNC addresses both the ill-posed inverse problem and the sensitivity distribution by dynamically allocating neural representational capacity to regions with lower sensitivity, ensuring accurate and balanced conductivity reconstructions. Extensive evaluations on both simulated and experimental data demonstrate that PhyNC outperforms existing methods in terms of detail preservation and artifact resistance, particularly in low-sensitivity regions. Our approach enhances the robustness of EIT reconstructions and provides a flexible framework that can be adapted to other imaging modalities with similar challenges.

Figures (12)

• Figure 1: Overview of PhyNC.a, The PhyNC model learns a continuous mapping from coordinates to their corresponding conductivity values using a neural field parameterized by an MLP and Hybrid representation. b, Each input coordinate $(x, y)$ is assigned to a specific level $l$ based on its intrinsic physical properties, forming the triplet $(x, y, l)$. c, Mip-Map embeddings are computed using grids with corresponding resolutions at each level. In parallel, Fourier feature projections are applied at each level with the appropriate frequencies. Addtionally, an global feature is concatenated with the aforementioned two components to enhance stability during reconstruction. d, The physics model projects the conductivity map onto a voltage signal. The loss is calculated between the measured data and the computed voltage to optimize the parameters of the PhyNC model.
• Figure 2: Toy initial sensitivity visualizations of Hash (left) and our PhyNC (right). The EIT physics model exhibits location-dependent sensitivity, which diminishes in regions farther from the electrodes. Consequently, Hash—using identical neural representation across all coordinates—naturally inherits this limitation and struggles to capture fine-grained details in these low-sensitivity areas. In contrast, PhyNC assigns higher-sensitivity neural representation to such regions, effectively compensating for the physics model's inherent constraints.
• Figure 3: Results on simulated data.a, Conductivity maps reconstructed by PhyNC and the baseline methods. Our method effectively recovers local details while maintaining background consistency. b, Spectral measurements comparing the proposed approach with our baselines on case 1 are presented, including illustrations and metrics for Frequency Band Correspondence. c, Reconstruction results on low-contrast simulated data demonstrate that our method effectively eliminates the staircase artifacts in the central area. The color bar is displayed on the right.
• Figure 4: Location-dependent sensitivity effects on reconstruction performance. Reconstruction results for two small triangles at varying locations from the center.
• Figure 5: Quantitative evaluation. The top row presents the reconstruction quality across all methods at each location using PSNR, SSIM, and LPIPS metrics. The bottom row displays three-segment piecewise linear fits for PhyNC (solid black lines), which delineate two critical distance thresholds (vertical dashed black lines).