3D image reconstruction algorithm for electrical impedance tomography data collected on planar electrode arrays

Abstract

Electrical Impedance Tomography (EIT) is a non-invasive, portable and low cost technology with many potential practical applications in medicine, geophysics and industry. In this paper, we present a three-dimensional non-iterative reconstruction algorithm suitable for breast cancer imaging. The reconstruction method is intended to be used for conductivity imaging with real data obtained from a planar EIT device developed recently at the University of Mainz, Germany. Although similar to the one described in, the novelty of the device, and hence of the reconstruction method proposed, consists in the distinct use of active and passive electrodes, i.e. there are 18 large active electrodes where the currents are injected and 66 point-like high impedance passive electrodes where the induced potentials are measured. The device has a fixed geometry, the positions of the electrodes are exactly known and there are no issues related to the contact impedance Two 2D non-iterative algorithms for imaging conductivity at the surface using the Mainz tomograph were described in. Numerical reconstructions had very good spatial resolution, and the algorithms were robust with respect to errors in the data. A sparsity enforcing three-dimensional reconstruction method using an adapted complete electrode model was also applied to this new planar EIT device in. Although promising, this iterative procedure proved to be quite demanding computationally and sensitive to the choice of the regularization parameter. The purpose of the current paper is to respond to these concerns by developing a simple and direct reconstruction algorithm to image the region beneath the electrode array. The approach is based on linearising the conductivity distribution about a constant approximation which reduces the computational demands. Although similar to the one in, the novelty of the proposed method consists in the distinct use of active and passive electrodes. Reconstructions from simulated data obtained using EIDORS are presented. At low frequencies, the electromagnetic field induced by applying a current density to the surface of the body is governed the generalized Laplace’s equation.