A quadratic model for inverse profiling: the one-dimensional case

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Abstract
In this paper a quadratic model for inverse profiling is introduced. It extends the range of validity of the linear (Born) method, and at the same time allows to manage the intrinsic non linearity of the problem. The inversion of the quadratic operator is based on the minimization of a proper defined functional involving both measured data and unknowns. The adopted geometrical approach, already used in the context of phase retrieval in antennas applications, avoids the occurrence of local minima. Numerical experiments, showing the good performances of the proposed method, are also presented.