  This paper proposes a nonlinear weighted anisotropic 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 by employing a novel soft thresholding based reformulation
included in the alternating direction method of multipliers (ADMM). To evaluate
the proposed approach, 2D and 3D numerical experiments 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 approaches. Owing to the simplicity
of the proposed method, the computational cost is significantly decreased
compared with the well established primal-dual algorithm. 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.
