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This paper proposes a nonlinear weighted anisotropic total variation (NWATV)regularization technique for electrical impedance tomography (EIT). The keyidea is to incorporate the internal inhomogeneity information (e.g., edges ofthe detected objects) into the EIT reconstruction process, aiming to preservethe conductivity profiles (to be detected). We study the NWATV imagereconstruction by employing a novel soft thresholding based reformulationincluded in the alternating direction method of multipliers (ADMM). To evaluatethe proposed approach, 2D and 3D numerical experiments and human EIT lungimaging are carried out. It is demonstrated that the properties of the internalinhomogeneity are well preserved and improved with the proposed regularizationapproach, in comparison to traditional total variation (TV) and recentlyproposed fidelity embedded regularization approaches. Owing to the simplicityof the proposed method, the computational cost is significantly decreasedcompared with the well established primal-dual algorithm. Meanwhile, it wasfound that the proposed regularization method is quite robust to themeasurement noise, which is one of the main uncertainties in EIT.

A nonlinear weighted anisotropic total variation regularization for electrical impedance tomography