Geometric shape characterization-based algorithm for electrical impedance tomography reconstruction

Abstract

Due to the advantages of B-spline curves in geometric modeling, this paper proposes an electrical impedance tomography (EIT) reconstruction algorithm based on geometric shape characterization (GSC). First, the method uses Density-Based Spatial Clustering of Applications with Noise (DBSCAN) to estimate the number and location of unknown inclusions within the measurement field. Based on this information, the conductivity reconstruction is formulated as an optimization problem involving the adjustment of B-spline curve control points, which is then solved iteratively using the Gauss–Newton (GN) and Levenberg–Marquardt (LM) algorithms. Both simulation and experimental results demonstrate that, compared to traditional image reconstruction methods, the B-spline-based approach enhances reconstructed image quality while preserving detail features of inclusions. Additionally, it achieves better reconstruction performance and noise robustness, with quantitative metrics such as the Spearman correlation coefficient, SSIM, and overlap rate consistently exceeding 0.9. The introduction of B-spline curves to construct regularization terms or to provide prior information reduces the ill-posedness and uncertainty of the inversion, thereby improving the quality and stability of the results. The code is available at GitHub.