Electrical impedance tomography with piecewise polynomial conductivities (Q2277797)

The reconstruction of a two-dimensional conductivity distribution leads to a nonlinear inverse problem for a two-dimensional elliptic equation with Neumann boundary conditions. A reconstruction algorithm is presented based on an iterative linearization. The conductivity is approximated by piecewise polynomials, based on Lagrange polynomials with local support. For the inverse problem the Gauss-Newton method is used. An important detail of the method is an algorithm to calculate efficiently the Jacobian matrix.