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This report extends our recent progress in tackling a challenging 3D inversescattering problem governed by the Helmholtz equation. Our target applicationis to reconstruct dielectric constants, electric conductivities and shapes offront surfaces of objects buried very closely under the ground. These objectsmimic explosives, like, e.g., antipersonnel land mines and improvised explosivedevices. We solve a coefficient inverse problem with the backscattering datagenerated by a moving source at a fixed frequency. This scenario has beenstudied so far by our newly developed convexification method that consists in anew derivation of a boundary value problem for a coupled quasilinear ellipticsystem. However, in our previous work only the unknown dielectric constants ofobjects and shapes of their front surfaces were calculated. Unlike this, in thecurrent work performance of our numerical convexification algorithm is verifiedfor the case when the dielectric constants, the electric conductivities andthose shapes of objects are unknown. By running several tests withexperimentally collected backscattering data, we find that we can accuratelyimage both the dielectric constants and shapes of targets of interestsincluding a challenging case of targets with voids. The computed electricalconductivity serves for reliably distinguishing conductive and non-conductiveobjects. The global convergence of our numerical procedure is shortlyrevisited.

An inverse problem of a simultaneous reconstruction of the dielectric constant and conductivity from experimental backscattering data