Experimental validation of a novel reconstruction algorithm for electrical impedance tomography based on backprojection of Lagrange multipliers

Abstract

A novel approach to image reconstruction for electrical impedance tomography (EIT) has been developed. It is based on a constrained optimization technique for the reconstruction of difference resistivity images without finite-element modelling. It solves the inverse problem by optimizing a cost function under constraints, in the form of normalized boundary potentials. Its application to the neighbouring data collection method is presented here. Mathematical models are developed according to specified criteria. These express the reconstructed image in terms of one-dimensional Lagrange multiplier functions. The reconstruction problem becomes one of estimating these functions from normalized boundary potentials. This model is based on a cost criterion of the minimization of the variance between the reconstructed and the true resistivity distributions. The algorithm was tested on data collected in a cylindrical saline-filled tank. A polyacrylamide rod was placed in various positions with or without a peripheral plaster of Paris ring in place. This was intended to resemble the conditions during EIT of epileptic seizures recorded with scalp or cortical electrodes in the human head. One advantage of this approach is that compensation for non-uniform initial conditions may be made, as this is a significant problem in imaging cerebral activity through the skull.