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arXiv · 2605.28392

Bound-Constrained Sparse Representation for Electrical Impedance Tomography

Chun Zhang·Dong Liu
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Abstract

This study proposes a bound-constrained sparse representation (BC-SR) framework for electrical impedance tomography (EIT), aimed at improving conductivity estimation without explicit regularization. BC-SR adopts a representation-driven strategy, generating conductivity from low-dimensional latent variables via an implicit composite parameterization. Structural priors are embedded using a truncated graph-Laplacian basis, while a bound-preserving nonlinear mapping enforces admissible conductivity ranges and improves conditioning through implicit gradient modulation. The approach ensures robust convergence, even under noisy or incomplete data. Extensive validation on 2D/3D simulations, tank experiments, and in-vivo lung data shows that BC-SR improves physical consistency and structural fidelity, offering enhanced robustness compared to traditional methods. Additionally, BC-SR enables 3D time-difference EIT reconstruction, offering improved spatial resolution and a more coherent representation of 3D conductivity distributions, particularly for in-vivo lung data. This suggests potential for improved performance in EIT, particularly in clinical applications for respiratory monitoring.

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Chun Zhang, Dong Liu. 2026-05-27. Bound-Constrained Sparse Representation for Electrical Impedance Tomography. https://arxiv.org/abs/2605.28392

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