Imaging of a rotationally symmetric dielectric cylinder by a quadratic approach

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Abstract
A quadratic approximation of the electromagnetic scattering equation isused to solve the inverse problem of the reconstruction of the dielectricpermittivity function of a rotationally symmetric cylindrical object embeddedin a homogeneous medium and illuminated by an incident plane wave at fixedfrequency. The problem is formulated as the minimization of a properly definedfunctional. Because the operator involved in the inversion is quadratic, itis possible to discuss and avoid the presence of local minima (a well-knownproblem in nonlinear inversion). Theoretical considerations and numericalexamples show the advantages of using a quadratic model in comparison witha linear one.