Joint sparsity recovery method for the EIT problem to reconstruct anomalies

This paper considers an electrical impedance tomography (EIT) problem to reconstruct multiple small anomalies from boundary measurements. The inverse problem of EIT is a severely ill-posed nonlinear inverse problem so that the conventional methods usually require linear approximation or iterative procedure. In this paper, we propose a non-iterative reconstruction method by exploiting the joint sparsity to attack these problems. It consists of three steps; first, the target location and corresponding current values are reconstructed using the joint sparse recovery. Second, the unknown potential is estimated, and conductivities are calculated as a final step. The advantages of the proposed method over conventional approaches are accuracy and speed, and we validate these effectiveness of the proposed algorithm by numerical simulations.