无需显式正则化，用约束稀疏表示提升电导率成像精度。
Bound-Constrained Sparse Representation for Electrical Impedance Tomography
- 通过隐式参数化从低维潜变量生成电导率分布。
- 在噪声和数据不全条件下仍能稳定收敛，2D/3D实验均表现更优。
- 适合临床肺部动态监测，可实现高保真3D时差成像。
本研究提出一种边界约束稀疏表示（BC-SR）框架用于电导率断层成像（EIT），旨在无需显式正则化即可提升电导率估计性能。BC-SR采用表征驱动策略，通过隐式复合参数化从低维潜变量生成电导率分布；利用截断图拉普拉斯基底嵌入结构先验，并通过保持边界的非线性映射确保电导率取值合理，同时通过隐式梯度调制改善条件性。该方法在2D/3D仿真、水槽实验及活体肺部数据上广泛验证，显著提升物理一致性与结构保真度，相较于传统方法更具鲁棒性。此外，BC-SR支持3D时差EIT重建，提升了空间分辨率，对活体肺部数据的三维电导率分布呈现更连贯，显示出在呼吸监测等临床应用中的潜力。
原文摘要 · Abstract (English)
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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