A Trust Region Subproblem for 3d Electrical Impedance Tomography Inverse Problem Using Experimental Data

Abstract

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 illposed 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.Corresponding author: M. Soleimani (m.soleimani@bath.ac.uk).

Multi-Resolution Retrieval of Non-Measurable Equivalent Currents in Microwave Imaging Problems-Experimental Assessment

“…However, only a few techniques have been proposed [3,4] to recover the contribute of the non-measurable currents from measured field data. The lack of information on these components results in too inaccurate reconstructions that generally suffer from a strong low-pass effect [2,14]. Since the achievable spatial resolution is strictly related to the number of basis functions modeling the unknowns, the higher is the spatial resolution the greater is the number of basis functions required to obtain accurate reconstructions.…”

“…Many strategies in microwave imaging reformulate the arising inverse scattering problem as the solution of an equivalent inverse source problem to determine either the profiles [4] or the dielectric properties [2][3][4] of unknown objects embedded in an inaccessible region. Despite the linearity of the inverse source problem with respect to the unknown equivalent current density within the investigation domain [5][6][7], the problem still remains ill-posed in the sense of Hadamard [11].…”

“…The retrieval of unknown targets embedded in inaccessible regions is a problem still actual and of interest [1] that need the development of efficient and reliable procedures for their application to real world problems [2,3,[27][28][29][30][31]. Many strategies in microwave imaging reformulate the arising inverse scattering problem as the solution of an equivalent inverse source problem to determine either the profiles [4] or the dielectric properties [2][3][4] of unknown objects embedded in an inaccessible region.…”

Two FFT Subspace-Based Optimization Methods for Electrical Impedance Tomography

“…Electrical impedance tomography has attracted intense interests recently in both mathematical and engineering fields [1,2]. It is well-know that EIT is a very challenging problem due to its nonlinear and highly ill-posed properties [3,4].…”

Absolute Imaging of Low Conductivity Material Distributions Using Nonlinear Reconstruction Methods in Magnetic Induction Tomography

“…Here, an adaptive process that is justified is applied to change this parameter during iterations with the intent to improve convergence. The process is automated and no time consuming traditional methods like the L-curve [16], which have been used in EIT [17], need to be applied. In this paper, the interest is also directed to examine the performance of two other nonlinear optimization methods namely: the Levenberg Marquardt method (LMM) and Powell Dog Leg method (PDLM).…”