Eigenfunction contrast source inversion for circular metallic enclosures

The microwave imaging problem is considered where an object of interest is surrounded by a circular metallic enclosure. A new contrast source inversion (CSI) algorithm which uses eigenfunction expansions of the unknowns is presented for the reconstruction of the complex dielectric profile. Orthonormal eigenfunction expansions associated with the Helmholtz operator for a homogeneous medium and Dirichlet boundary conditions are used for the unknown contrast source and the contrast functions in the CSI functional. These are also used to express the incident field, which is assumed known, as well as for expanding the inverse Helmholtz operator in the CSI functional. The imaging domain is taken to be the whole interior of the metallic enclosure. No prior information, other than keeping the permittivity profile physical, is used. Results are provided for synthetic as well as experimental data. Based on the number of eigenfunctions used, a theoretical limit to the reconstruction quality is defined. Normalized errors relative to this theoretical limit are provided for each of the synthetic data sets