A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data

Abstract

Image reconstruction in electrical impedance tomography (EIT) is an ill-posed nonlinear inverse problem. Regularization methods are needed to solve this problem. The results of the ill-posed EIT problem strongly depends on noise level in measured data as well as regularization parameter. In this paper, we present trust region subproblem (TRS), with the use of L-curve maximum curvature criteria to find a regularization parameter. Currently Krylov subspace methods especially conjugate gradient least squares (CGLS) are used for large scale 3D problem. CGLS is an efficient technique when the norm of measured noise is exactly known. This paper demonstrates that CGLS and TRS converge to the same point on the L-curve with the same noise level. TRS can be implemented efficiently for large scale inverse EIT problem as CGLS with no need a priori knowledge of the noise level.