A nonlinear weighted anisotropic total variation regularization for electrical impedance tomography

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.