Bound-Constrained Sparse Representation for Electrical Impedance Tomography.

OBJECTIVE: To develop a stable and physically constrained framework for absolute electrical impedance tomography (EIT) reconstruction. METHODS: A bound constrained sparse representation (BC-SR) framework is proposed to embed structural and physical priors directly into the conductivity parameterization. A truncated graph Laplacian basis provides a low-dimensional representation, while a nonlinear bound-preserving mapping enforces prescribed conductivity ranges. The resulting latent variables are reconstructed using nonlinear optimization on 2D and 3D unstructured meshes. RESULTS: Experiments involving ablation and noise-robustness studies, 2D, 2.5D, and 3D numerical simulations, and tank measurements show that BC-SR suppresses unstable artifacts and improves structural fidelity and physical consistency compared with conventional reconstruction methods. CONCLUSION: BC-SR improves the stability of absolute EIT reconstruction by constraining both the effective solution space and the admissible conductivity values. SIGNIFICANCE: BC-SR enables the effective reconstruction dimension to be selected independently of the FEM mesh resolution and reduces dependence on case-specific regularization-weight tuning, providing a broadly applicable framework for 2D and 3D EIT on unstructured meshes.