Full three-dimensional multi-frequency electromagnetic inversion

A method is presented for reconstructing the permittivity and conductivity of unknown 3D targets embedded in a lossy homogeneous background from vectorial multi-frequency data. The unknown targets are assumed to be located in an object domain D embedded in a homogeneous lossy background medium with complex conductivity /spl sigma//sub b/'=/spl sigma//sub b/-i/spl omega//sub j//spl epsiv//sub b/ To reconstruct the complex conductivity of this object domain D from knowledge of the scattered field, we assume that the targets are illuminated successively by a number of incident fields generated by dipole sources at different spatial positions (k=1, ..., K) and operating at different frequencies (j=1, ..., J). We then have a full-vectorial three-dimensional problem where the incident electric field is denoted by E/sub j,k//sup inc/, and the total electric field by E/sub j,k/. We assume that, for the description of the material dispersion, the Maxwell model holds. We then introduce the contrast function /spl chi//sub j/=(/spl epsiv/-/spl epsiv//sub b/)//spl epsiv//sub b/+i(/spl sigma/-/spl sigma//sub b/)//spl omega//sub j//spl epsiv//sub b/, where /spl epsiv/ is the spatially dependent permittivity and /spl sigma/ is the spatially dependent conductivity.