Implicit Neural Shape Optimization for 3D High-Contrast Electrical Impedance Tomography
This addresses high-contrast EIT scenarios for medical imaging with metallic implants and industrial defect detection, representing a novel method for a known bottleneck.
The paper tackles the problem of 3D high-contrast Electrical Impedance Tomography (EIT) where conductivity has sharp discontinuities, which is challenging for traditional methods. It presents an implicit neural shape optimization framework that demonstrates substantial performance improvements through numerical experiments.
We present a novel implicit neural shape optimization framework for 3D high-contrast Electrical Impedance Tomography (EIT), addressing scenarios where conductivity exhibits sharp discontinuities across material interfaces. These high-contrast cases, prevalent in metallic implant monitoring and industrial defect detection, challenge traditional reconstruction methods due to severe ill-posedness. Our approach synergizes shape optimization with implicit neural representations, introducing key innovations including a shape derivative-based optimization scheme that explicitly incorporates high-contrast interface conditions and an efficient latent space representation that reduces variable dimensionality. Through rigorous theoretical analysis of algorithm convergence and extensive numerical experiments, we demonstrate substantial performance improvements, establishing our framework as promising for practical applications in medical imaging with metallic implants and industrial non-destructive testing.