AN EXACTLY-SOLVABLE QUASISTATIC ELECTRICITY INVERSE PROBLEM: RETRIEVAL OF THE COMPLEX PERMITTIVITY OF A CYLINDER TAKING ACCOUNT OF NUISANCE PARAMETER UNCERTAINTY

International audience—This study concerns the 2D inverse problem of the retrieval, using external eld data, ofeither one of the two physical parameters, constituted by the real and imaginary parts of the permittivity,of a z-independent cylindrical dielectric specimen subjected to an external, z-independent, quasistaticelectric eld. Six other parameters enter into the inverse problem. They are termed nuisance parametersbecause: 1) they are not retrieved during the inversion and 2) uncertainty as to their actual values canadversely aect the accuracy of the retrieval of the permittivity. This inverse problem is shown tohave an exact, mathematically-explicit, solution, both for continuous and discrete input data, whoseproperties, with respect to the various nuisance parameter uncertainties, are analyzed for noiseless data.It is found that: a) optimal inversion requires data registered at only a small number of sensors, b)the inverse solution, satisfying pre-existing physical constraints, exists and is unique. Moreover, theinverse solution is shown to be unstable with respect to three nuisance parameter uncertainties, theconsequence of which is large retrieval inaccuracy for small nuisance parameter uncertainties, actingeither individually or in combination