Existence and uniqueness of a solution to the inverse problem of the complex permittivity reconstruction of a dielectric body in a waveguide

Abstract

This paper presents a statement, a proof of uniqueness, and a method of solution to the inverse problem of the determination of permittivity of a lossy dielectric inclusion in a three-dimensional waveguide of rectangular cross-section from the transmission characteristics. The approach is based on the solution to a volume singular integral equation (VSIE). The examination of this equation is based on the analysis of the corresponding boundary value problem (BVP) for the system of Maxwell's equations and the equivalence of this BVP and VSIE. The existence and uniqueness for VSIE in the space of square-integrable functions are proved. The permittivity reconstruction employs a method of iterations applied to the solution of VSIE.