A Second-Order Generalized Total Variation with Improved Alternating Direction Method of Multipliers Algorithm for Electrical Impedance Tomography Reconstruction

Abstract

The issue of Electrical Impedance Tomography (EIT) is a well-known inverse problem that presents challenging characteristics. In order to address the difficulties associated with ill-conditioned inverses, regularization methods are typically employed. One commonly used approach is total variation (TV) regularization, which has shown effectiveness in EIT. In order to meet the requirements of real-time tracking, it is essential to acquire fast and reliable algorithms for image reconstruction. Therefore, we present a modified second-order generalized regularization algorithm that enables more-accurate reconstruction of organ boundaries and internal structures, to reduce EIT artifacts, and to overcome the inability of the conventional Tikhonov regularization method in solving the step effect of the medium boundary. The proposed algorithm uses the improved alternating direction method of multipliers (ADMM) to tackle this optimization issue and adopts the second-order generalized total variation (SOGTV) function with strong boundary-preserving features as the regularization generalization function. The experiments are based on simulation data and the physical model of the circular water tank that we developed. The results showed that SOGTV regularization can improve image realism compared with some classic regularization.

Keywords

• electrical impedance tomography
• generalized total variation
• TV regularization
• inverse problems