A Nonlinear Weighted Anisotropic Total Variation Regularization for Electrical Impedance Tomography

This article proposes a nonlinear weighted anisotro- pic total variation (NWATV) regularization technique for electrical impedance tomography (EIT). The key idea is to incorporate the internal inhomogeneity information (e.g., edges of the detected objects) into the EIT reconstruction process, aiming to preserve the conductivity profiles (to be detected). We study the NWATV image reconstruction using a novel soft thresholding-based reformulation included in the alternating direction method of multipliers (ADMM). To evaluate the proposed approach, numerical simulations and human EIT lung imaging are carried out. It is demonstrated that the properties of the internal inhomogeneity are well-preserved and improved with the proposed regularization approach, in comparison to traditional total variation (TV) and recently proposed fidelity embedded regularization (FER) approaches. Owing to the simplicity of the proposed method, the computational cost is significantly decreased compared with the well-established primal-dual algorithm. Precisely, with the proposed algorithm, we are able to alleviate the staircase effect arising in TV regularization and improve the reconstruction accuracy for FER does. To achieve similar accuracy as TV does, the computational times are reduced from 2.311 to 0.629 and 1.733 to 0.428 s in 2-D and 3-D simulations, respectively, and the computational time is reduced from greater than 2 s to less than 0.2 s in the human experiment. Meanwhile, it was found that the proposed regularization method is quite robust to the measurement noise, which is one of the main uncertainties in EIT.