A Krylov subspace type method for Electrical Impedance Tomography

Abstract

Electrical Impedance Tomography (EIT) is a well-known imaging technique for detecting the electrical properties of an object in order to detect anomalies, such as conductive or resistive targets. More specifically, EIT has many applications in medical imaging for the detection and location of bodily tumors since it is an affordable and non-invasive method, which aims to recover the internal conductivity of a body using voltage measurements resulting from applying low frequency current at electrodes placed at its surface. Mathematically, the reconstruction of the internal conductivity is a severely ill-posed inverse problem and yields a poor quality image reconstruction. To remedy this difficulty, at least in part, we regularize and solve the nonlinear minimization problem by the aid of a Krylov subspace-type method for the linear sub problem during each iteration. In EIT, a tumor or general anomaly can be modeled as a piecewise constant perturbation of a smooth background, hence, we solve the regularized problem on a subspace of relatively small dimension by the Flexible Golub-Kahan process that provides solutions that have sparse representation. For comparison, we use a well-known modified Gauss-Newton algorithm as a benchmark. Using simulations, we demonstrate the effectiveness of the proposed method. The obtained reconstructions indicate that the Krylov subspace method is better adapted to solve the ill-posed EIT problem and results in higher resolution images and faster convergence compared to reconstructions using the modified Gauss-Newton algorithm.

Imaging of Insect Hole in Living Tree Trunk Based on Joint Driven Algorithm of Electromagnetic Inverse Scattering

“…The accuracy of the inversion results was evaluated according to Formula (16). The results are shown in Table 3, which demonstrates that under the condition of maintaining the Inversion Ratio, changing the radius will not affect the accuracy value.…”

“…One type is the linearization of nonlinear problems, represented by the Born and Rytov approximations [12,13], which have very good imaging results for Low dielectric constants. Another type of inversion method is the nonlinear method [14], which uses an iterative idea to improve the inversion accuracy through continuous iteration; the main methods are the Contrast Source Inversion (CSI) and the Subspace Optimization Method (SOM) [15,16]. Although these nonlinear iterative methods improve accuracy compared to linear approximation methods, they have disadvantages such as sensitivity to initial values and slow convergence [17].…”

Nonlinear Electrical Impedance Tomography Method Using a Complete Electrode Model for the Characterization of Heterogeneous Domains

“…There are similar EIT approaches developed so far, but they mostly deal with Neumann or Dirichlet boundary conditions to solve the forward problem [17][18][19]. Some recent studies have included the Robin boundary condition to reflect the contact impedance between the domain and electrode boundaries, but their inverse formulation and optimization schemes are different from the present study [20,21].…”