Graduate Seminar

Scheduled Talk - September 9, 2009 - [ 12:00PM in DH 1064 ]

Alexander Mamonov

"Resistor Network Approaches to the Numerical Solution of Electrical Impedance Tomography with Partial Boundary Measurements"

Abstract:
Electrical Impedance Tomography (EIT) is a problem of finding the electrical conductivity inside a physical body from simultaneous measurements of voltages and currents on its boundary. If only a part of the body's boundary is available for measurements, we refer to such case as the partial boundary measurements. Even in the case of full boundary measurements the problem is known to be severely ill-conditioned, which makes inversion difficult. A typical method of solving the EIT would be using some form of regularized optimization algorithm. We propose a different approach based on the theory of resistor networks and optimal grids. Such an approach has already been shown to solve the full boundary measurement problem efficiently. We present two distinct methods of solving the partial measurement problem based on different resistor network topologies and the theory of (quasi-) conformal mappings. Extensive numerical results are given for both approaches.