TITLE:  Electric Impedance Tomography with Resistor Networks

SPEAKER:  FERNANDO GUEVARA VASQUEZ

AFFILIATION:  Department of Mathematics, Stanford University


Electric impedance tomography consists in finding the
conductivity inside a body from electrical measurements taken
at its surface. This is a severely ill-posed problem: any
numerical inversion scheme requires some form of
regularization. We present inversion schemes that address the
instability of the problem with a reduced model approach,
where the reduced models are resistor networks that arise in
the finite volumes discretization of the forward problem.
Specifically, we consider finite volume grids of size
determined by the measurement precision, but where the node
locations are determined adaptively. We show that the model
reduction problem of finding the smallest resistor network (of
fixed topology) that can predict measurements of the
Dirichlet-to-Neumann map is uniquely solvable for a broad
class of measurements. We view the model reduction as a
nonlinear map of the data.  Numerical evidence suggests this
map acts as an approximate inverse of the forward map. To
image the conductivity we use this map as a preconditioner in
a Newton type iteration. A priori information can be easily
incorporated to the method.