Rima Gandlin, Department of Mathematical Sciences, Carnegie Mellon University
"Two Multigrid Algorithms for Inverse Problem in Electrical Impedance Tomography (EIT)"
An EIT device for medical use consists of a set of electrodes attached to the patient? chest. The collected data are then used to compute the conductivity distribution and then to display it on a screen in order to detect anomalies, such as tumors. The conductivity depends on the EIT data in a very weak way. In this sense the inverse problem of EIT is ill-posed. The ill-posedness of an inverse problem does not necessarily imply more expensive solution process. On the contrary: once the nature of the ill-posedness has been generally understood, to solve an inverse problem may even be much less expensive than to solve a corresponding direct problem. For this specific EIT problem two multigrid algorithms were developed, one uses the classical regularizaton technique, the other regularizes itself by careful choice of grids. Second algorithm is a new type of a multigrid algorithm, involving near-boundary semi-coarsening cycles within full-coarsening cycles. Both algorithms give nearly the same accuracy, but the second algorithm is much cheaper since it does not have all those artificial regularization parameters as the first algorithm does.
TUESDAY, February 17, 2004