A nonlinear weighted anisotropic total variation regularization for electrical impedance tomography

TL;DR

This paper introduces a nonlinear weighted anisotropic total variation regularization method for electrical impedance tomography that effectively preserves internal inhomogeneities, reduces computational cost, and enhances robustness against measurement noise.

Contribution

The paper presents a novel NWATV regularization technique with a soft thresholding reformulation within ADMM, improving EIT reconstructions over traditional methods.

Findings

Better preservation of internal inhomogeneity features.

Reduced computational cost compared to primal-dual algorithms.

Robustness to measurement noise in EIT reconstructions.

Abstract

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.