Image reconstruction using the modified Newton Raphson algorithm for electrical impedance tomography based on finite element medhod

Abstract

Electrical Impedance Tomography (EIT), a noninvasive imagingmethod. is now beeing considered as complementary to other imagingtechniques such as x-ray, ultrasound. gamma camera. etc.E.I.T. injects constant current (20kHz to 50kHz) into the body.usmg a pair of surface electrodes and measures the resulting voltagesbetween all other peripheral adjacent electrodes. arranged in pairs. toestimate body's internal resistivity distribution.For the reconstruction of body resistivity Image. the forwardproblem is solved first. by representing the body with a Finite-Elementmodel. For this purpose, the region of interest is divided into small discretetriangular elements assuming that the resistivity in each element ishomogenous. 3-layer. 56 element mesh structure and 16 peripheral nodes(electrodes) is used to simulate the resistivity distribution and the finiteelement model has been developed for known circular and elliptical regions.To solve the inverse problem. the modified Newton-Raphsonmethod is used as an iterative reconstruction method. The inherent illconditioningin the approximate Hessian matrix of the linearized system ofequations for the resistivity update is eliminated using the Singular ValueDecomposition technique.All reconstruction algorithms start with homogenous initial guessthen finds reconstructed images using single anomaly at every layer,centerly located anomalies and mUltiple anomalies.Reconstructed images with the modified Newton-Raphson andimproved Perturbation methods are compared. Although Perturbationmethod is faster, the Modified Newton-Raphson convergence is found to bemuch better requiring a small number of iterations.