🤖 AI Summary
In 3D high-contrast electrical impedance tomography (EIT), severe interface distortions arise in reconstructions due to strong ill-posedness induced by abrupt conductivity discontinuities—e.g., at metal implant–tissue or defect–material boundaries. To address this, we propose a 3D shape optimization framework based on implicit neural representations (signed distance function networks). Our method introduces, for the first time, a variational optimization scheme integrated with shape derivatives to explicitly encode high-contrast interface conditions. We further design a low-dimensional latent-space implicit shape representation that ensures geometric fidelity while improving parameter efficiency. Theoretical analysis guarantees convergence. Extensive 3D simulations and hardware-in-the-loop experiments demonstrate a 42% reduction in average interface localization error and significantly enhanced reconstruction stability. These results validate the framework’s effectiveness and practical potential for medical monitoring of metallic implants and industrial non-destructive testing.
📝 Abstract
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.