Simultaneous nonlinear inversion of permeability and permittivity in two dimensions using time-domain data

The authors solve the nonlinear two-dimensional electromagnetic inverse problem, taking into account the spatial variations of permeability as well as those of permittivity. They formulate the problem as a volume integral equation for the scattered field, with scattering contributions from two unknown object functions. The inverse problem is solved by starting from the Born approximations and performing iterations on the integral equation. The forward problem is solved once during each iteration. For the two-unknown-function (permeability and permittivity) problem, the inversion procedure is carried out via a double-criterion optimization. Eight transmitters and eight receivers are used, and several permittivity and permeability profile are reconstructed.<>