Adaptive Reconstruction for Electrical Impedance Tomography with a Piecewise Constant Conductivity
For researchers in inverse problems, this work provides a theoretically grounded adaptive algorithm for EIT, but it is incremental as it combines existing techniques (Tikhonov regularization, Modica-Mortola penalty, adaptive mesh refinement) without major breakthroughs.
The paper proposes an adaptive mesh refinement method for electrical impedance tomography to recover piecewise constant conductivity, proving convergence of the algorithm and demonstrating its behavior with numerical examples.
In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a Modica-Mortola penalty functional and adaptive mesh refinement using suitable a posteriori error estimators of residual type that involve the state, adjoint and variational inequality in the necessary optimality condition and a separate marking strategy. We prove the convergence of the adaptive algorithm in the following sense: the sequence of discrete solutions contains a subsequence convergent to a solution of the continuous necessary optimality system. Several numerical examples are presented to illustrate the convergence behavior of the algorithm.