Inverse method for imaging a free surface using electrical impedance tomography

The feasibility of inverting measurements from electrical impedance tomogra phy (EIT) to image the free surface of a homogeneous conductor within an op en channel is investigated. Potential measurements from a linear array of e lectrodes placed at the bottom of the channel are simulated using a finite element method. The simulated measurements are inverted using an iterative, sometimes weighted, least-squares method to give an approximation to the h eight of the conductor as a function of position. The inverse problem is no t well-posed and is also ill-conditioned. To pose the problem properly the free surface is either described by a global parameterization or a local, p iecewise parameterization, where in both cases the number of coefficients i s limited to the number of measurements. To overcome the ill-conditioning e ither the Marquardt method or nth-order regularization is implemented. The effects of measurement protocol (number of electrodes and current pattern) and measurement noise are also examined. The global parameterization using: Chebyshev polynomials was successful, whereas inverses utilizing the local ized parameterization failed to return acceptable images of the free surfac e. In the majority of cases examined, the Marquardt method for solving iter ative least-squares problems gave more accurate solutions than any of the r egularization methods within the first 100 iterations. Among the regulariza tion methods, first-order regularization out-performed both the zeroth- and second-order regularizations. Inverses of data collected with the opposite measurement protocol generally required a fewer number of iterations to re ach an acceptable solution than the adjacent measurement protocol, and solv ing the inverse problem using an overdetermined system was found to be adva ntageous. Reconstructing the free surface from noisy measurements was possi ble with a moderate amount of noise, and using a weighted least-squares met hod was better than a non-weighted method for noisy sets of data. (C) 1999 Elsevier Science Ltd. All rights reserved.