A Matlab toolkit for three-dimensional electrical impedance tomography: a contribution to the Electrical Impedance and Diffuse Optical Reconstruction Software project

Abstract

The objective of the Electrical Impedance and Diffuse Optical Reconstruction Software project is to develop freely available software that can be used to reconstruct electrical or optical material properties from boundary measurements. Nonlinear and ill posed problems such as electrical impedance and optical tomography are typically approached using a finite element model for the forward calculations and a regularized nonlinear solver for obtaining a unique and stable inverse solution. Most of the commercially available finite element programs are unsuitable for solving these problems because of their conventional inefficient way of calculating the Jacobian, and their lack of accurate electrode modelling. A complete package for the two-dimensional EIT problem was officially released by Vauhkonen et al at the second half of 2000. However most industrial and medical electrical imaging problems are fundamentally three-dimensional. To assist the development we have developed and released a free toolkit of Matlab routines which can be employed to solve the forward and inverse EIT problems in three dimensions based on the complete electrode model along with some basic visualization utilities, in the hope that it will stimulate further development. We also include a derivation of the formula for the Jacobian (or sensitivity) matrix based on the complete electrode model.

The impact of electrode area, contact impedance and boundary shape on EIT images

“…For a CEM spanning multiple edges on the FEM mesh boundary, there must be a distribution of the contact impedance amongst those edges. One method of distributing the contact impedance is to use a linear expansion function that assigns the contact impedance based on the length between nodes in two dimensions or area of a boundary element in three dimensions as in (Polydorides & Lionheart 2002). Because contact impedance is typically specified in units that include geometry, the location of the FEM nodes for the electrode must accurately reflect the total area of the electrode to achieve the correct overall electrode impedance.…”

An Image Reconstruction Algorithm for Electrical Impedance Tomography Using Adaptive Group Sparsity Constraint

“…Two weighting strategies are considered, i.e., weighting based on Eq. (20) and weighting using all one vector. Fig.…”

“…The result validates that by giving a smaller weight to the large group and a larger weight to the small group as formulated by the weighting strategy in Eq. (20), the imaging quality can be further improved as the sparsity of the estimation is promoted.…”

“…Another prevailing studies based on direct methods, such as the dbar method and Calderon method, were also reported for electrical tomography to obtain the gray value of reconstructed image directly and independently [16][17][18][19]. In addition, an open-source Matlab toolkit named EIDORS was developed and has been widely used for three-dimensional EIT image reconstruction problems in the past decades [20], which integrates the most commonly used EIT image reconstruction algorithms. Beyond that, the comprehensive review of the state-of-the-art EIT image reconstruction algorithms is also well summarized and thoroughly discussed in [21] and [22].…”

Addressing the computational cost of large EIT solutions

“…The matrix of these perturbation experiments forms the Jacobian matrix. More efficient algorithms to estimate the Jacobian exist such as the self-adjoint method (Breckon, 1990;Polydorides and Lionheart, 2002). Another such trick is to remember that the Jacobian only considers the effect at the electrodes, so a significant reduction in computation time can be achieved by applying a QR decomposition to the set of all unit stimulations forming the right-hand side.…”